# Amicable pairs

Amicable pairs
You are encouraged to solve this task according to the task description, using any language you may know.

Two integers ${\displaystyle N}$ and ${\displaystyle M}$ are said to be amicable pairs if ${\displaystyle N\neq M}$ and the sum of the proper divisors of ${\displaystyle N}$ (${\displaystyle \mathrm {sum} (\mathrm {propDivs} (N))}$) ${\displaystyle =M}$ as well as ${\displaystyle \mathrm {sum} (\mathrm {propDivs} (M))=N}$.

Example

1184 and 1210 are an amicable pair, with proper divisors:

•   1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592   and
•   1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605   respectively.

Calculate and show here the Amicable pairs below 20,000; (there are eight).

## 11l

F sum_proper_divisors(n)
R I n < 2 {0} E sum((1 .. n I/ 2).filter(it -> (@n % it) == 0))

L(n) 1..20000
V m = sum_proper_divisors(n)
I m > n & sum_proper_divisors(m) == n
print(n"\t"m)

## 8080 Assembly

	org	100h
;;;	Calculate proper divisors of 2..20000
lxi	h,pdiv + 4	; 2 bytes per entry
lxi	d,19999		; [2 .. 20000] means 19999 entries
lxi	b,1		; Initialize each entry to 1
init:	mov	m,c
inx	h
mov	m,b
inx	h
dcx	d
mov	a,d
ora	e
jnz	init
lxi	b,1		; BC = outer loop variable
iouter:	inx	b
lxi	h,-10001	; Are we there yet?
jc	idone		; If so, we've calculated all of them
mov	h,b
mov	l,c
xchg			; DE = inner loop variable
iinner:	push	d		; save DE
xchg
lxi	d,pdiv
mov	e,m		; DE = pdiv[DE]
inx	h
mov	d,m
xchg			; pdiv[DE] += BC
xchg			; store it back
mov	m,d
dcx	h
mov	m,e
pop	h		; restore DE (into HL)
lxi	d,-20001	; are we there yet?
jc	iouter		; then continue with outer loop
lxi	d,20001		; otherwise continue with inner loop
xchg
jmp	iinner
idone:	lxi	b,1		; BC = outer loop variable
touter:	inx	b
lxi	h,-20001	; Are we there yet?
rc			; If so, stop
mov	d,b		; DE = outer loop variable
mov	e,c
tinner:	inx	d
lxi	h,-20001	; Are we there yet?
jc	touter		; If so continue with outer loop
push	d		; Store the variables
push	b
mov	h,b		; find *pdiv[BC]
mov	l,c
lxi	b,pdiv
mov	a,m		; Compare low byte (to E)
cmp	e
jnz	tnext1		; Not equal = not amicable
inx	h
mov	a,m
cmp	d		; Compare high byte (to B)
jnz	tnext1		; Not equal = not amicable
pop	b		; Restore BC
xchg			; find *pdiv[DE]
lxi	d,pdiv
mov	a,m		; Compare low byte (to C)
cmp	c
jnz	tnext2		; Not equal = not amicable
inx	h
mov	a,m		; Compare high byte (to B)
cmp 	b
jnz	tnext2		; Not equal = not amicable
pop	d		; Restore DE
push	d		; Save them both on the stack again
push	b
push 	d
mov	h,b		; Print the first number
mov	l,c
call	prhl
pop 	h		; And the second number
call	prhl
lxi	d,nl		; And a newline
mvi	c,9
call 	5
tnext1:	pop	b		; Restore B
tnext2:	pop	d		; Restore D
jmp	tinner		; Continue
;;;	Print the number in HL
prhl:	lxi	d,nbuf		; Store buffer pointer on stack
push 	d
lxi	b,-10		; Divisor
pdgt:	lxi	d,-1		; Quotient
pdivlp:	inx	d
jc	pdivlp
mvi	a,'0'+10	; Make ASCII digit
pop	h		; Store in output buffer
dcx	h
mov	m,a
push	h
xchg			; Keep going with rest of number
mov	a,h		; if not zero
ora	l
jnz	pdgt
mvi	c,9		; CP/M call to print string
pop	d		; Get buffer pointer
jmp	5
db	'*****'
nbuf:	db	' $' nl: db 13,10,'$'
pdiv:	equ	$; base Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 ## 8086 Assembly LIMIT: equ 20000 ; Maximum value cpu 8086 org 100h section .text mov ax,final ; Set DS and ES to point just beyond the mov cl,4 ; program. We're just going to assume MS-DOS shr ax,cl ; gave us enough memory. (Generally the case, inc ax ; a .COM gets a 64K segment and we need ~40K.) mov cx,cs add ax,cx mov ds,ax mov es,ax calc: mov ax,1 ; Calculate proper divisors for 2..20000 mov di,4 ; Initially, set each entry to 1. mov cx,LIMIT-1 ; 2 to 20000 inclusive = 19999 entries rep stosw mov ax,2 ; AX = outer loop counter mov cl,2 mov dx,LIMIT*2 ; Keep inner loop limit ready in DX mov bp,LIMIT/2 ; And outer loop limit in BP .outer: mov bx,ax ; BX = inner loop counter (multiplied by two) shl bx,cl ; Each entry is 2 bytes wide .inner: add [bx],ax ; divsum[BX/2] += AX add bx,ax ; Advance to next entry add bx,ax ; Twice, because each entry is 2 bytes wide cmp bx,dx ; Are we there yet? jbe .inner ; If not, keep going inc ax cmp ax,bp ; Is the outer loop done yet? jbe .outer ; If not, keep going show: mov dx,LIMIT ; Keep limit ready in DX mov ax,2 ; AX = outer loop counter mov si,4 ; SI = address for outer loop .outer: mov cx,ax ; CX = inner loop counter inc cx mov di,cx ; DI = address for inner loop shl di,1 mov bx,[si] ; Preload divsum[AX] .inner: cmp cx,bx ; CX == divsum[AX]? jne .next ; If not, the pair is not amicable cmp ax,[di] ; AX == divsum[CX]? jne .next ; If not, the pair is not amicable push ax ; Keep the registers push bx push cx push dx push cx ; And CX twice because we need to print it call prax ; Print the first number pop ax call prax ; And the second number mov dx,nl ; And a newline call pstr pop dx ; Restore the registers pop cx pop bx pop ax .next: inc di ; Increment inner loop variable and address inc di ; Address twice because each entry has 2 bytes inc cx cmp cx,dx ; Are we done yet? jbe .inner ; If not, keep going inc si ; Increment outer loop variable and address inc si ; Address twice because each entry has 2 bytes inc ax cmp ax,dx ; Are we done yet? jbe .outer ; If not, keep going. ret ;;; Print the number in AX. Destroys AX, BX, CX, DX. prax: mov cx,10 ; Divisor mov bx,nbuf ; Buffer pointer .digit: xor dx,dx div cx ; Divide by 10 and extract digit add dl,'0' ; Add ASCII 0 to digit dec bx mov [cs:bx],dl ; Store in string test ax,ax ; Any more? jnz .digit ; If so, keep going mov dx,bx ; If not, print the result ;;; Print string from CS. pstr: push ds ; Save DS mov ax,cs ; Set DS to CS mov ds,ax mov ah,9 ; Print string using MS-DOS int 21h pop ds ; Restore DS ret db '*****' nbuf: db '$'
nl:	db	13,10,'$' final: equ$

Output:
220 284
1184 1210
2620 2924
5020 5564
6232 6368
10744 10856
12285 14595
17296 18416

## AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits
or android 64 bits with application Termux
/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program amicable64.s   */

/*******************************************/
/* Constantes file                         */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"

.equ NMAXI,      20000
.equ TABMAXI,      100

/*********************************/
/* Initialized data              */
/*********************************/
.data
sMessResult:        .asciz " @ : @\n"
szCarriageReturn:   .asciz "\n"
szMessErr1:         .asciz "Array too small !!"
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:                  .skip 24
tResult:                    .skip 8 * TABMAXI
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                             // entry of program
mov x4,#2                     // number begin
1:
mov x0,x4                     // number
bl decFactor                  // compute sum factors
cmp x0,x4                     // equal ?
beq 2f
mov x2,x0                     // factor sum 1
bl decFactor
cmp x0,x4                     // equal number ?
bne 2f
mov x0,x4                     // yes -> search in array
mov x1,x2                     // and store sum
bl searchRes
cmp x0,#0                     // find ?
bne 2f                        // yes
mov x0,x4                     // no -> display number ans sum
mov x1,x2
bl displayResult
2:
cmp x4,x3                     // end ?
ble 1b

100:                              // standard end of the program
mov x0, #0                    // return code
mov x8, #EXIT                 // request to exit program
svc #0                        // perform the system call
/***************************************************/
/*   display message number                        */
/***************************************************/
/* x0 contains number 1           */
/* x1 contains number 2               */
displayResult:
stp x1,lr,[sp,-16]!           // save  registers
stp x2,x3,[sp,-16]!           // save  registers
mov x2,x1
bl conversion10               // call décimal conversion
ldr x1,qAdrsZoneConv          // insert conversion in message
bl strInsertAtCharInc
mov x3,x0
mov x0,x2
bl conversion10               // call décimal conversion
mov x0,x3
ldr x1,qAdrsZoneConv          // insert conversion in message
bl strInsertAtCharInc

bl affichageMess              // display message
ldp x2,x3,[sp],16              // restaur  2 registers
ldp x1,lr,[sp],16              // restaur  2 registers
/***************************************************/
/*   compute factors sum                        */
/***************************************************/
/* x0 contains the number            */
decFactor:
stp x1,lr,[sp,-16]!       // save  registers
stp x2,x3,[sp,-16]!       // save  registers
stp x4,x5,[sp,-16]!       // save  registers
mov x4,#1                 // init sum
mov x1,#2                 // start factor -> divisor
1:
udiv x2,x0,x1
msub x3,x2,x1,x0          // remainder
cmp x1,x2                 // divisor > quotient ?
bgt 3f
cmp x3,#0                 // remainder = 0 ?
bne 2f
cmp x1,x2                 // divisor = quotient ?
beq 3f                    // yes -> end
2:
b 1b                      // and loop
3:
mov x0,x4                 // return sum
ldp x4,x5,[sp],16         // restaur  2 registers
ldp x2,x3,[sp],16         // restaur  2 registers
ldp x1,lr,[sp],16         // restaur  2 registers
/***************************************************/
/*   search and store result in array                        */
/***************************************************/
/* x0 contains the number            */
/* x1 contains factors sum           */
/* x0 return 1 if find 0 else  -1 if error      */
searchRes:
stp x1,lr,[sp,-16]!       // save  registers
stp x2,x3,[sp,-16]!       // save  registers
stp x4,x5,[sp,-16]!       // save  registers
mov x2,#0                 // indice begin
1:
ldr x3,[x4,x2,lsl #3]     // load one result array
cmp x3,#0                 // if 0 store new result
beq 2f
cmp x3,x0                 // equal ?
beq 3f                    // find -> return 1
cmp x2,#TABMAXI           // maxi array ?
blt 1b
bl affichageMess
mov x0,#-1
b 100f
2:
str x1,[x4,x2,lsl #3]
mov x0,#0                 // not find -> store and retun 0
b 100f
3:
mov x0,#1
100:
ldp x4,x5,[sp],16         // restaur  2 registers
ldp x2,x3,[sp],16         // restaur  2 registers
ldp x1,lr,[sp],16         // restaur  2 registers
/********************************************************/
/*        File Include fonctions                        */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"
 220 : 284
1184 : 1210
2620 : 2924
5020 : 5564
6232 : 6368
10744 : 10856
12285 : 14595
17296 : 18416


## ABC

HOW TO RETURN proper.divisor.sum.table n:
PUT {} IN propdivs
FOR i IN {1..n}: PUT 1 IN propdivs[i]
FOR i IN {2..floor (n/2)}:
PUT i+i IN j
WHILE j<=n:
PUT propdivs[j] + i IN propdivs[j]
PUT i + j IN j
RETURN propdivs

PUT 20000 IN maximum
PUT proper.divisor.sum.table maximum IN propdivs

FOR cand IN {1..maximum}:
PUT propdivs[cand] IN other
IF cand<other<maximum AND propdivs[other]=cand:
WRITE cand, other/
Output:
220 284
1184 1210
2620 2924
5020 5564
6232 6368
10744 10856
12285 14595
17296 18416

## Action!

Calculations on a real Atari 8-bit computer take quite long time. It is recommended to use an emulator capable with increasing speed of Atari CPU.

INCLUDE "H6:SIEVE.ACT"

CARD FUNC SumDivisors(CARD x)
CARD i,max,sum

sum=1 i=2 max=x
WHILE i<max
DO
IF x MOD i=0 THEN
max=x/i
IF i<max THEN
sum==+i+max
ELSEIF i=max THEN
sum==+i
FI
FI
i==+1
OD
RETURN (sum)

PROC Main()
DEFINE MAXNUM="20000"
BYTE ARRAY primes(MAXNUM+1)
CARD m,n

Put(125) PutE() ;clear the screen
Sieve(primes,MAXNUM+1)
FOR m=1 TO MAXNUM-1
DO
IF primes(m)=0 THEN
n=SumDivisors(m)
IF n<MAXNUM AND primes(n)=0 AND n>m THEN
IF m=SumDivisors(n) THEN
PrintF("%U %U%E",m,n)
FI
FI
FI
OD
RETURN
Output:
220 284
1184 1210
2620 2924
5020 5564
6232 6368
10744 10856
12285 14595
17296 18416


This solution uses the package Generic_Divisors from the Proper Divisors task [[1]].

with Ada.Text_IO, Generic_Divisors; use Ada.Text_IO;

procedure Amicable_Pairs is

function Same(P: Positive) return Positive is (P);

package Divisor_Sum is new Generic_Divisors
(Result_Type => Natural, None => 0, One => Same, Add =>  "+");

Num2 : Integer;
begin
for Num1 in 4 .. 20_000 loop
Num2 := Divisor_Sum.Process(Num1);
if Num1 < Num2 then
if Num1 = Divisor_Sum.Process(Num2) then
Put_Line(Integer'Image(Num1) & "," & Integer'Image(Num2));
end if;
end if;
end loop;
end Amicable_Pairs;

Output:
 220, 284
1184, 1210
2620, 2924
5020, 5564
6232, 6368
10744, 10856
12285, 14595
17296, 18416


## ALGOL 60

Works with: A60
begin

comment - return n mod m;
integer procedure mod(n, m);
value n, m; integer n, m;
begin
mod := n - m * entier(n / m);
end;

comment - return sum of the proper divisors of n;
integer procedure sumf(n);
value n; integer n;
begin
integer sum, f1, f2;
sum := 1;
f1 := 2;
for f1 := f1 while (f1 * f1) <= n do
begin
if mod(n, f1) = 0 then
begin
sum := sum + f1;
f2 := n / f1;
if f2 > f1 then sum := sum + f2;
end;
f1 := f1 + 1;
end;
sumf := sum;
end;

comment - main program begins here;
integer a, b, found;
outstring(1,"Searching up to 20000 for amicable pairs\n");
found := 0;
for a := 2 step 1 until 20000 do
begin
b := sumf(a);
if b > a then
begin
if a = sumf(b) then
begin
found := found + 1;
outinteger(1,a);
outinteger(1,b);
outstring(1,"\n");
end;
end;
end;
outinteger(1,found);
outstring(1,"pairs were found");

end
Output:
Searching up to 20000 for amicable pairs
220  284
1184  1210
2620  2924
5020  5564
6232  6368
10744  10856
12285  14595
17296  18416
8 pairs were found


## ALGOL 68

BEGIN # find amicable pairs p1, p2 where each is equal to the other's proper divisor sum #
[ 1 : 20 000 ]INT pd sum; # table of proper divisors #
FOR n TO UPB pd sum DO pd sum[ n ] := 1 OD;
FOR i FROM 2 TO UPB pd sum
DO FOR j FROM i + i BY i TO UPB pd sum DO
pd sum[ j ] +:= i
OD
OD;
# find the amicable pairs up to 20 000                            #
FOR p1 TO UPB pd sum - 1 DO
INT pd sum p1 = pd sum[ p1 ];
IF pd sum p1 > p1 AND pd sum p1 <= UPB pd sum THEN
IF pd sum[ pd sum p1 ] = p1 THEN
print( ( whole( p1, -6 ), " and ", whole( pd sum p1, -6 ), " are an amicable pair", newline ) )
FI
FI
OD
END
Output:
   220 and    284 are an amicable pair
1184 and   1210 are an amicable pair
2620 and   2924 are an amicable pair
5020 and   5564 are an amicable pair
6232 and   6368 are an amicable pair
10744 and  10856 are an amicable pair
12285 and  14595 are an amicable pair
17296 and  18416 are an amicable pair


## ALGOL W

Translation of: ALGOL 68
begin % find amicable pairs p1, p2 where each is equal to the other's      %
% proper divisor sum                                                 %

integer MAX_NUMBER;
MAX_NUMBER := 20000;

begin
integer array pdSum( 1 :: MAX_NUMBER ); % table of proper divisors %
for i := 1 until MAX_NUMBER do pdSum( i ) := 1;
for i := 2 until MAX_NUMBER do begin
for j := i + i step i until MAX_NUMBER do pdSum( j ) := pdSum( j ) + i
end for_i ;

% find the amicable pairs up to 20 000                             %
for p1 := 1 until MAX_NUMBER - 1 do begin
integer pdSumP1;
pdSumP1 := pdSum( p1 );
if pdSumP1 > p1 and pdSumP1 <= MAX_NUMBER and pdSum( pdSumP1 ) = p1 then begin
write( i_w := 5, s_w := 0, p1, " and ", pdSumP1, " are an amicable pair" )
end if_pdSumP1_gt_p1_and_le_MAX_NUMBER
end for_p1
end
end.
Output:
  220 and   284 are an amicable pair
1184 and  1210 are an amicable pair
2620 and  2924 are an amicable pair
5020 and  5564 are an amicable pair
6232 and  6368 are an amicable pair
10744 and 10856 are an amicable pair
12285 and 14595 are an amicable pair
17296 and 18416 are an amicable pair


## AppleScript

### Functional

Translation of: JavaScript
-- AMICABLE PAIRS ------------------------------------------------------------

-- amicablePairsUpTo :: Int -> Int
on amicablePairsUpTo(max)

-- amicable :: [Int] -> Int -> Int -> [Int] -> [Int]
script amicable
on |λ|(a, m, n, lstSums)
if (m > n) and (m ≤ max) and ((item m of lstSums) = n) then
a & [[n, m]]
else
a
end if
end |λ|
end script

-- divisorsSummed :: Int -> Int
-- sum :: Int -> Int -> Int
script sum
on |λ|(a, b)
a + b
end |λ|
end script

on |λ|(n)
foldl(sum, 0, properDivisors(n))
end |λ|
end script

foldl(amicable, {}, ¬
end amicablePairsUpTo

-- TEST ----------------------------------------------------------------------
on run

amicablePairsUpTo(20000)

end run

-- PROPER DIVISORS -----------------------------------------------------------

-- properDivisors :: Int -> [Int]
on properDivisors(n)

-- isFactor :: Int -> Bool
script isFactor
on |λ|(x)
n mod x = 0
end |λ|
end script

-- integerQuotient :: Int -> Int
script integerQuotient
on |λ|(x)
(n / x) as integer
end |λ|
end script

if n = 1 then
{1}
else
set realRoot to n ^ (1 / 2)
set intRoot to realRoot as integer
set blnPerfectSquare to intRoot = realRoot

-- Factors up to square root of n,
set lows to filter(isFactor, enumFromTo(1, intRoot))

-- and quotients of these factors beyond the square root,
-- excluding n itself (last item)
items 1 thru -2 of (lows & map(integerQuotient, ¬
items (1 + (blnPerfectSquare as integer)) thru -1 of reverse of lows))
end if
end properDivisors

-- GENERIC FUNCTIONS ---------------------------------------------------------

-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m > n then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo

-- filter :: (a -> Bool) -> [a] -> [a]
on filter(f, xs)
tell mReturn(f)
set lst to {}
set lng to length of xs
repeat with i from 1 to lng
set v to item i of xs
if |λ|(v, i, xs) then set end of lst to v
end repeat
return lst
end tell
end filter

-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn

Output:
{{220, 284}, {1184, 1210}, {2620, 2924}, {5020, 5564},
{6232, 6368}, {10744, 10856}, {12285, 14595}, {17296, 18416}}


### Straightforward

… and about 55 times as fast as the above.

on properDivisors(n)
set output to {}

if (n > 1) then
set sqrt to n ^ 0.5
set limit to sqrt div 1
if (limit = sqrt) then
set end of output to limit
set limit to limit - 1
end if
repeat with i from limit to 2 by -1
if (n mod i is 0) then
set beginning of output to i
set end of output to n div i
end if
end repeat
set beginning of output to 1
end if

return output
end properDivisors

on sumList(listOfNumbers)
script o
property l : listOfNumbers
end script
set sum to 0
repeat with n in o's l
set sum to sum + n
end repeat

return sum
end sumList

on amicablePairsBelow(limitPlus1)
script o
property pdSums : {missing value} -- Sums of proper divisors. (Dummy item for 1's.)
end script
set limit to limitPlus1 - 1
repeat with n from 2 to limit
set end of o's pdSums to sumList(properDivisors(n))
end repeat

set output to {}
repeat with n1 from 2 to (limit - 1)
set n2 to o's pdSums's item n1
if ((n1 < n2) and (n2 < limitPlus1) and (o's pdSums's item n2 = n1)) then ¬
set end of output to {n1, n2}
end repeat

return output
end amicablePairsBelow

on join(lst, delim)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delim
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join

set output to amicablePairsBelow(20000)
repeat with thisPair in output
set thisPair's contents to join(thisPair, " & ")
end repeat
return join(output, linefeed)


Output:
"220 & 284
1184 & 1210
2620 & 2924
5020 & 5564
6232 & 6368
10744 & 10856
12285 & 14595
17296 & 18416"


## ARM Assembly

Works with: as version Raspberry Pi
or android 32 bits with application Termux
/* ARM assembly Raspberry PI or android with termux */
/*  program amicable.s   */

/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly
for the routine affichageMess conversion10
see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes                       */
/************************************/
.include "../constantes.inc"

.equ NMAXI,      20000
.equ TABMAXI,      100

/*********************************/
/* Initialized data              */
/*********************************/
.data
sMessResult:        .asciz " @ : @\n"
szCarriageReturn:   .asciz "\n"
szMessErr1:         .asciz "Array too small !!"
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:                  .skip 24
tResult:                    .skip 4 * TABMAXI
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                             @ entry of program
mov r4,#2                     @ number begin
1:
mov r0,r4                     @ number
bl decFactor                  @ compute sum factors
cmp r0,r4                     @ equal ?
beq 2f
mov r2,r0                     @ factor sum 1
bl decFactor
cmp r0,r4                     @ equal number ?
bne 2f
mov r0,r4                     @ yes -> search in array
mov r1,r2                     @ and store sum
bl searchRes
cmp r0,#0                     @ find ?
bne 2f                        @ yes
mov r0,r4                     @ no -> display number ans sum
mov r1,r2
bl displayResult
2:
cmp r4,r3                     @ end ?
ble 1b

100:                              @ standard end of the program
mov r0, #0                    @ return code
mov r7, #EXIT                 @ request to exit program
svc #0                        @ perform the system call
iNMaxi:                       .int NMAXI
/***************************************************/
/*   display message number                        */
/***************************************************/
/* r0 contains number 1           */
/* r1 contains number 2               */
displayResult:
push {r1-r3,lr}               @ save registers
mov r2,r1
bl conversion10               @ call décimal conversion
ldr r1,iAdrsZoneConv          @ insert conversion in message
bl strInsertAtCharInc
mov r3,r0
mov r0,r2
bl conversion10               @ call décimal conversion
mov r0,r3
ldr r1,iAdrsZoneConv          @ insert conversion in message
bl strInsertAtCharInc

bl affichageMess              @ display message
pop {r1-r3,pc}                @ restaur des registres
/***************************************************/
/*   compute factors sum                        */
/***************************************************/
/* r0 contains the number            */
decFactor:
push {r1-r5,lr}           @ save registers
mov r5,#1                 @ init sum
mov r4,r0                 @ save number
mov r1,#2                 @ start factor -> divisor
1:
mov r0,r4                 @ dividende
bl division
cmp r1,r2                 @ divisor > quotient ?
bgt 3f
cmp r3,#0                 @ remainder = 0 ?
bne 2f
cmp r1,r2                 @ divisor = quotient ?
beq 3f                    @ yes -> end
2:
b 1b                      @ and loop
3:
mov r0,r5                 @ return sum
pop {r1-r5,pc}            @ restaur registers
/***************************************************/
/*   search and store result in array                        */
/***************************************************/
/* r0 contains the number            */
/* r1 contains factors sum           */
/* r0 return 1 if find 0 else  -1 if error      */
searchRes:
push {r1-r4,lr}              @ save registers
mov r2,#0                    @ indice begin
1:
ldr r3,[r4,r2,lsl #2]        @ load one result array
cmp r3,#0                    @ if 0 store new result
beq 2f
cmp r3,r0                    @ equal ?
moveq r0,#1                  @ find -> return 1
beq 100f
cmp r2,#TABMAXI              @ maxi array ?
blt 1b
bl affichageMess
mov r0,#-1
b 100f
2:
str r1,[r4,r2,lsl #2]
mov r0,#0                   @ not find -> store and retun 0
100:
pop {r1-r4,pc}              @ restaur registers
/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../affichage.inc"
 220         : 284
1184        : 1210
2620        : 2924
5020        : 5564
6232        : 6368
10744       : 10856
12285       : 14595
17296       : 18416


## Arturo

properDivs: function [x] ->
(factors x) -- x

amicable: function [x][
y: sum properDivs x
if and? x = sum properDivs y
x <> y
-> return @[x,y]
return ø
]

amicables: []

loop 1..20000 'n [
am: amicable n
if am <> ø
-> 'amicables ++ @[sort am]
]

print unique amicables

Output:
[220 284] [1184 1210] [2620 2924] [5020 5564] [6232 6368] [10744 10856] [12285 14595] [17296 18416]

## ATS

(* ****** ****** *)
//
#include
#include
//
(* ****** ****** *)
//
fun
sum_list_vt
(xs: List_vt(int)): int =
(
case+ xs of
| ~list_vt_nil() => 0
| ~list_vt_cons(x, xs) => x + sum_list_vt(xs)
)
//
(* ****** ****** *)

fun
propDivs
(
x0: int
) : List0_vt(int) =
loop(x0, 2, list_vt_sing(1)) where
{
//
fun
loop
(
x0: int, i: int, res: List0_vt(int)
) : List0_vt(int) =
(
if
(i * i) > x0
then list_vt_reverse(res)
else
(
if x0 % i != 0
then
loop(x0, i+1, res)
// end of [then]
else let
val res =
cons_vt(i, res)
// end of [val]
val res =
(
if i * i = x0 then res else cons_vt(x0 / i, res)
) : List0_vt(int) // end of [val]
in
loop(x0, i+1, res)
end // end of [else]
// end of [if]
)
) (* end of [loop] *)
//
} // end of [propDivs]

(* ****** ****** *)

fun
sum_propDivs(x: int): int = sum_list_vt(propDivs(x))

(* ****** ****** *)

val
theNat2 = auxmain(2) where
{
fun
auxmain
(
n: int
) : stream_vt(int) = $ldelay(stream_vt_cons(n, auxmain(n+1))) } (* ****** ****** *) // val theAmicable = ( stream_vt_takeLte(theNat2, 20000) ).filter() ( lam x => let val x2 = sum_propDivs(x) in x < x2 && x = sum_propDivs(x2) end ) // (* ****** ****** *) val () = theAmicable.foreach() ( lam x => println! ("(", x, ", ", sum_propDivs(x), ")") ) (* ****** ****** *) implement main0 () = () (* ****** ****** *) Output: (220, 284) (1184, 1210) (2620, 2924) (5020, 5564) (6232, 6368) (10744, 10856) (12285, 14595) (17296, 18416)  ## AutoHotkey SetBatchLines -1 Loop, 20000 { m := A_index ; Getting factors loop % floor(sqrt(m)) { if ( mod(m, A_index) = 0 ) { if ( A_index ** 2 == m ) { sum += A_index continue } else if ( A_index != 1 ) { sum += A_index + m//A_index } else if ( A_index = 1 ) { sum += A_index } } } ; Factors obtained ; Checking factors of sum if ( sum > 1 ) { loop % floor(sqrt(sum)) { if ( mod(sum, A_index) = 0 ) { if ( A_index ** 2 == sum ) { sum2 += A_index continue } else if ( A_index != 1 ) { sum2 += A_index + sum//A_index } else if ( A_index = 1 ) { sum2 += A_index } } } if ( m = sum2 ) && ( m != sum ) && ( m < sum ) final .= m . ":" . sum . "n" } ; Checked sum := 0 sum2 := 0 } MsgBox % final ExitApp  Output: 220:284 1184:1210 2620:2924 5020:5564 6232:6368 10744:10856 12285:14595 17296:18416  ## AWK #!/bin/awk -f function sumprop(num, i,sum,root) { if (num < 2) return 0 sum=1 root=sqrt(num) for ( i=2; i < root; i++) { if (num % i == 0 ) { sum = sum + i + num/i } } if (num % root == 0) { sum = sum + root } return sum } BEGIN{ limit=20000 print "Amicable pairs < ",limit for (n=1; n < limit+1; n++) { m=sumprop(n) if (n == sumprop(m) && n < m) print n,m } } }  Output: # ./amicable Amicable pairs < 20000 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  ## BASIC ### ANSI BASIC Translation of: GFA Basic Works with: Decimal BASIC 100 DECLARE EXTERNAL FUNCTION sum_proper_divisors 110 CLEAR 120 ! 130 DIM f(20001) ! sum of proper factors for each n 140 FOR i=1 TO 20000 150 LET f(i)=sum_proper_divisors(i) 160 NEXT i 170 ! look for pairs 180 FOR i=1 TO 20000 190 FOR j=i+1 TO 20000 200 IF f(i)=j AND i=f(j) THEN 210 PRINT "Amicable pair ";i;" ";j 220 END IF 230 NEXT j 240 NEXT i 250 ! 260 PRINT 270 PRINT "-- found all amicable pairs" 280 END 290 ! 300 ! Compute the sum of proper divisors of given number 310 ! 320 EXTERNAL FUNCTION sum_proper_divisors(n) 330 ! 340 IF n>1 THEN ! n must be 2 or larger 350 LET sum=1 ! start with 1 360 LET root=SQR(n) ! note that root is an integer 370 ! check possible factors, up to sqrt 380 FOR i=2 TO root 390 IF MOD(n,i)=0 THEN 400 LET sum=sum+i ! i is a factor 410 IF i*i<>n THEN ! check i is not actual square root of n 420 LET sum=sum+n/i ! so n/i will also be a factor 430 END IF 440 END IF 450 NEXT i 460 END IF 470 LET sum_proper_divisors = sum 480 END FUNCTION  Output: Amicable pair 220 284 Amicable pair 1184 1210 Amicable pair 2620 2924 Amicable pair 5020 5564 Amicable pair 6232 6368 Amicable pair 10744 10856 Amicable pair 12285 14595 Amicable pair 17296 18416 -- found all amicable pairs  ### BASIC256 Translation of: FreeBASIC function SumProperDivisors(number) if number < 2 then return 0 sum = 0 for i = 1 to number \ 2 if number mod i = 0 then sum += i next i return sum end function dim sum(20000) for n = 1 to 19999 sum[n] = SumProperDivisors(n) next n print "The pairs of amicable numbers below 20,000 are :" print for n = 1 to 19998 f = sum[n] if f <= n or f < 1 or f > 19999 then continue for if f = sum[n] and n = sum[f] then print rjust(string(n), 5); " and "; sum[n] end if next n end Output: The pairs of amicable numbers below 20,000 are : 220 and 284 1184 and 1210 2620 and 2924 5020 and 5564 6232 and 6368 10744 and 10856 12285 and 14595 17296 and 18416 ### Chipmunk Basic Works with: Chipmunk Basic version 3.6.4 100 cls : rem 10 HOME for Applesoft BASIC 110 print "The pairs of amicable numbers below 20,000 are :" 120 print 130 size = 18500 140 for n = 1 to size 150 m = amicable(n) 160 if m > n and amicable(m) = n then 170 print using "#####";n; 180 print " and "; 190 print using "#####";m 200 endif 210 next 220 end 230 function amicable(nr) 240 suma = 1 250 for d = 2 to sqr(nr) 260 if nr mod d = 0 then suma = suma+d+nr/d 270 next 280 amicable = suma 290 end function  Output: Same as FreeBASIC entry. ### Gambas Translation of: FreeBASIC Public sum[19999] As Integer Public Sub Main() Dim n As Integer, f As Integer For n = 0 To 19998 sum[n] = SumProperDivisors(n) Next Print "The pairs of amicable numbers below 20,000 are :\n" For n = 0 To 19998 ' f = SumProperDivisors(n) f = sum[n] If f <= n Or f < 1 Or f > 19999 Then Continue If f = sum[n] And n = sum[f] Then Print Format$(Str$(n), "#####"); " And "; Format$(Str$(sum[n]), "#####") End If Next End Function SumProperDivisors(number As Integer) As Integer If number < 2 Then Return 0 Dim sum As Integer = 0 For i As Integer = 1 To number \ 2 If number Mod i = 0 Then sum += i Next Return sum End Function  Output: Same as FreeBASIC entry. ### QBasic Works with: QBasic version 1.1 Works with: QuickBasic version 4.5 FUNCTION amicable (nr) suma = 1 FOR d = 2 TO SQR(nr) IF nr MOD d = 0 THEN suma = suma + d + nr / d NEXT amicable = suma END FUNCTION PRINT "The pairs of amicable numbers below 20,000 are :" PRINT size = 18500 FOR n = 1 TO size m = amicable(n) IF m > n AND amicable(m) = n THEN PRINT USING "##### and #####"; n; m END IF NEXT END  Output: Same as FreeBASIC entry. ### True BASIC FUNCTION amicable(nr) LET suma = 1 FOR d = 2 TO SQR(nr) IF REMAINDER(nr, d) = 0 THEN LET suma = suma + d + nr / d END IF NEXT d LET amicable = suma END FUNCTION PRINT "The pairs of amicable numbers below 20,000 are :" PRINT LET size = 18500 FOR n = 1 TO size LET m = amicable(n) IF m > n AND amicable(m) = n THEN PRINT USING "##### and #####": n, m NEXT n END  Output: Same as FreeBASIC entry. ## BCPL get "libhdr" manifest$(
MAXIMUM = 20000
$) // Calculate proper divisors for 1..N let propDivSums(n) = valof$(  let v = getvec(n)
for i = 1 to n do v!i := 1
for i = 2 to n/2 do
$( let j = i*2 while j < n do$(  v!j := v!j + i
j := j + i
$)$)
resultis v
$) // Are A and B an amicable pair, given the list of sums of proper divisors? let amicable(pdiv, a, b) = a = pdiv!b & b = pdiv!a let start() be$(  let pds = propDivSums(MAXIMUM)
for x = 1 to MAXIMUM do
for y = x+1 to MAXIMUM do
if amicable(pds, x, y) do
writef("%N, %N*N", x, y)
$) Output: 220, 284 1184, 1210 2620, 2924 5020, 5564 6232, 6368 10744, 10856 12285, 14595 17296, 18416 ## Befunge v_@#-*8*:"2":$_:#!2#*8#g*#6:#0*#!:#-*#<v>*/.55+,
1>:28*:*:*%\28*:*:*/06p28*:*:*/\2v %%^:*:<>*v
+|!:-1g60/*:*:*82::+**:*:<<>:#**#8:#<*^>.28*^8 :
:v>>*:*%/\28*:*:*%+\v>8+#$^#_+#\:#0<:\1/*:*2#< 2v^:*82\/*:*:*82:::_v#!%%*:*:*82\/*:*:*82::<_^#< >>06p:28*:*:**1+01-\>1+::28*:*:*/\28*:*:*%:*\!^  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 ## C Remark: Look at Pascal Alternative [[2]].You are using the same principle, so here too both numbers of the pair must be < top. The program will overflow and error in all sorts of ways when given a commandline argument >= UINT_MAX/2 (generally 2^31) #include <stdio.h> #include <stdlib.h> typedef unsigned int uint; int main(int argc, char **argv) { uint top = atoi(argv[1]); uint *divsum = malloc((top + 1) * sizeof(*divsum)); uint pows[32] = {1, 0}; for (uint i = 0; i <= top; i++) divsum[i] = 1; // sieve // only sieve within lower half , the modification starts at 2*p for (uint p = 2; p+p <= top; p++) { if (divsum[p] > 1) { divsum[p] -= p;// subtract number itself from divisor sum ('proper') continue;} // p not prime uint x; // highest power of p we need //checking x <= top/y instead of x*y <= top to avoid overflow for (x = 1; pows[x - 1] <= top/p; x++) pows[x] = p*pows[x - 1]; //counter where n is not a*p with a = ?*p, useful for most p. //think of p>31 seldom divisions or p>sqrt(top) than no division is needed //n = 2*p, so the prime itself is left unchanged => k=p-1 uint k= p-1; for (uint n = p+p; n <= top; n += p) { uint s=1+pows[1]; k--; // search the right power only if needed if ( k==0) { for (uint i = 2; i < x && !(n%pows[i]); s += pows[i++]); k = p; } divsum[n] *= s; } } //now correct the upper half for (uint p = (top >> 1)+1; p <= top; p++) { if (divsum[p] > 1){ divsum[p] -= p;} } uint cnt = 0; for (uint a = 1; a <= top; a++) { uint b = divsum[a]; if (b > a && b <= top && divsum[b] == a){ printf("%u %u\n", a, b); cnt++;} } printf("\nTop %u count : %u\n",top,cnt); return 0; }  Output: % ./a.out 20000 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 Top 20000 count : 8 % ./a.out 524000000 .. 475838415 514823985 491373104 511419856 509379344 523679536 Top 524000000 count : 442 real 0m16.285s user 0m16.156s  ## C# using System; using System.Collections.Generic; using System.Linq; namespace RosettaCode.AmicablePairs { internal static class Program { private const int Limit = 20000; private static void Main() { foreach (var pair in GetPairs(Limit)) { Console.WriteLine("{0} {1}", pair.Item1, pair.Item2); } } private static IEnumerable<Tuple<int, int>> GetPairs(int max) { List<int> divsums = Enumerable.Range(0, max + 1).Select(i => ProperDivisors(i).Sum()).ToList(); for(int i=1; i<divsums.Count; i++) { int sum = divsums[i]; if(i < sum && sum <= divsums.Count && divsums[sum] == i) { yield return new Tuple<int, int>(i, sum); } } } private static IEnumerable<int> ProperDivisors(int number) { return Enumerable.Range(1, number / 2) .Where(divisor => number % divisor == 0); } } }  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  ## C++ #include <vector> #include <unordered_map> #include <iostream> int main() { std::vector<int> alreadyDiscovered; std::unordered_map<int, int> divsumMap; int count = 0; for (int N = 1; N <= 20000; ++N) { int divSumN = 0; for (int i = 1; i <= N / 2; ++i) { if (fmod(N, i) == 0) { divSumN += i; } } // populate map of integers to the sum of their proper divisors if (divSumN != 1) // do not include primes divsumMap[N] = divSumN; for (std::unordered_map<int, int>::iterator it = divsumMap.begin(); it != divsumMap.end(); ++it) { int M = it->first; int divSumM = it->second; int divSumN = divsumMap[N]; if (N != M && divSumM == N && divSumN == M) { // do not print duplicate pairs if (std::find(alreadyDiscovered.begin(), alreadyDiscovered.end(), N) != alreadyDiscovered.end()) break; std::cout << "[" << M << ", " << N << "]" << std::endl; alreadyDiscovered.push_back(M); alreadyDiscovered.push_back(N); count++; } } } std::cout << count << " amicable pairs discovered" << std::endl; }  Output: [220, 284] [1184, 1210] [2620, 2924] [5020, 5564] [6232, 6368] [10744, 10856] [12285, 14595] [17296, 18416] 8 amicable pairs discovered  ## Clojure (ns example (:gen-class)) (defn factors [n] " Find the proper factors of a number " (into (sorted-set) (mapcat (fn [x] (if (= x 1) [x] [x (/ n x)])) (filter #(zero? (rem n %)) (range 1 (inc (Math/sqrt n)))) ))) (def find-pairs (into #{} (for [n (range 2 20000) :let [f (factors n) ; Factors of n M (apply + f) ; Sum of factors g (factors M) ; Factors of sum N (apply + g)] ; Sum of Factors of sum :when (= n N) ; (sum(proDivs(N)) = M and sum(propDivs(M)) = N :when (not= M N)] ; N not-equal M (sorted-set n M)))) ; Found pair ;; Output Results (doseq [q find-pairs] (println q))  Output: #{220 284} #{6232 6368} #{1184 1210} #{5020 5564} #{2620 2924} #{12285 14595} #{17296 18416} #{10744 10856}  ## CLU % Generate proper divisors from 1 to max proper_divisors = proc (max: int) returns (array[int]) divs: array[int] := array[int]$fill(1, max, 0)
for i: int in int$from_to(1, max/2) do for j: int in int$from_to_by(i*2, max, i) do
divs[j] := divs[j] + i
end
end
return(divs)
end proper_divisors

% Are A and B and amicable pair, given the proper divisors?
amicable = proc (divs: array[int], a, b: int) returns (bool)
return(divs[a] = b & divs[b] = a)
end amicable

% Find all amicable pairs up to 20 000
start_up = proc ()
max = 20000
po: stream := stream$primary_output() divs: array[int] := proper_divisors(max) for a: int in int$from_to(1, max) do
for b: int in int$from_to(a+1, max) do if amicable(divs, a, b) then stream$putl(po, int$unparse(a) || ", " || int$unparse(b))
end
end
end
end start_up
Output:
220, 284
1184, 1210
2620, 2924
5020, 5564
6232, 6368
10744, 10856
12285, 14595
17296, 18416

## Common Lisp

(let ((cache (make-hash-table)))
(defun sum-proper-divisors (n)
(or (gethash n cache)
(setf (gethash n cache)
(loop for x from 1 to (/ n 2)
when (zerop (rem n x))
sum x)))))

(defun amicable-pairs-up-to (n)
(loop for x from 1 to n
for sum-divs = (sum-proper-divisors x)
when (and (< x sum-divs) (= x (sum-proper-divisors sum-divs)))
collect (list x sum-divs)))

(amicable-pairs-up-to 20000)

Output:
((220 284) (1184 1210) (2620 2924) (5020 5564) (6232 6368) (10744 10856)
(12285 14595) (17296 18416))

## Cowgol

include "cowgol.coh";

const LIMIT := 20000;

# Calculate sums of proper divisors
var divSum: uint16[LIMIT + 1];
var i: @indexof divSum;
var j: @indexof divSum;

i := 2;
while i <= LIMIT loop
divSum[i] := 1;
i := i + 1;
end loop;

i := 2;
while i <= LIMIT/2 loop
j := i * 2;
while j <= LIMIT loop
divSum[j] := divSum[j] + i;
j := j + i;
end loop;
i := i + 1;
end loop;

# Test each pair
i := 2;
while i <= LIMIT loop
j := i + 1;
while j <= LIMIT loop
if divSum[i] == j and divSum[j] == i then
print_i32(i as uint32);
print(", ");
print_i32(j as uint32);
print_nl();
end if;
j := j + 1;
end loop;
i := i + 1;
end loop;
Output:
220, 284
1184, 1210
2620, 2924
5020, 5564
6232, 6368
10744, 10856
12285, 14595
17296, 18416

## Crystal

MX = 524_000_000
N = Math.sqrt(MX).to_u32
x = Array(Int32).new(MX+1, 1)

(2..N).each { |i|
p = i*i
x[p] += i
k = i+i+1
(p+i..MX).step(i) { |j|
x[j] += k
k += 1
}
}

(4..MX).each { |m|
n = x[m]
if n < m && n != 0 && m == x[n]
puts "#{n} #{m}"
end
}

Output:
220 284
1184 1210
2620 2924
5020 5564
6232 6368
10744 10856
12285 14595
17296 18416
...... ......
....... .......
426191535 514780497
475838415 514823985
509379344 523679536


## D

Translation of: Python
void main() @safe /*@nogc*/ {
import std.stdio, std.algorithm, std.range, std.typecons, std.array;

immutable properDivs = (in uint n) pure nothrow @safe /*@nogc*/ =>
iota(1, (n + 1) / 2 + 1).filter!(x => n % x == 0);

enum rangeMax = 20_000;
auto n2d = iota(1, rangeMax + 1).map!(n => properDivs(n).sum);

foreach (immutable n, immutable divSum; n2d.enumerate(1))
if (n < divSum && divSum <= rangeMax && n2d[divSum - 1] == n)
writefln("Amicable pair: %d and %d with proper divisors:\n    %s\n    %s",
n, divSum, properDivs(n), properDivs(divSum));
}

Output:
Amicable pair: 220 and 284 with proper divisors:
[1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110]
[1, 2, 4, 71, 142]
Amicable pair: 1184 and 1210 with proper divisors:
[1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592]
[1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605]
Amicable pair: 2620 and 2924 with proper divisors:
[1, 2, 4, 5, 10, 20, 131, 262, 524, 655, 1310]
[1, 2, 4, 17, 34, 43, 68, 86, 172, 731, 1462]
Amicable pair: 5020 and 5564 with proper divisors:
[1, 2, 4, 5, 10, 20, 251, 502, 1004, 1255, 2510]
[1, 2, 4, 13, 26, 52, 107, 214, 428, 1391, 2782]
Amicable pair: 6232 and 6368 with proper divisors:
[1, 2, 4, 8, 19, 38, 41, 76, 82, 152, 164, 328, 779, 1558, 3116]
[1, 2, 4, 8, 16, 32, 199, 398, 796, 1592, 3184]
Amicable pair: 10744 and 10856 with proper divisors:
[1, 2, 4, 8, 17, 34, 68, 79, 136, 158, 316, 632, 1343, 2686, 5372]
[1, 2, 4, 8, 23, 46, 59, 92, 118, 184, 236, 472, 1357, 2714, 5428]
Amicable pair: 12285 and 14595 with proper divisors:
[1, 3, 5, 7, 9, 13, 15, 21, 27, 35, 39, 45, 63, 65, 91, 105, 117, 135, 189, 195, 273, 315, 351, 455, 585, 819, 945, 1365, 1755, 2457, 4095]
[1, 3, 5, 7, 15, 21, 35, 105, 139, 417, 695, 973, 2085, 2919, 4865]
Amicable pair: 17296 and 18416 with proper divisors:
[1, 2, 4, 8, 16, 23, 46, 47, 92, 94, 184, 188, 368, 376, 752, 1081, 2162, 4324, 8648]
[1, 2, 4, 8, 16, 1151, 2302, 4604, 9208]

See Pascal.

## Draco

/* Fill a given array such that for each N,
* P[n] is the sum of proper divisors of N */
proc nonrec propdivs([*] word p) void:
word i, j, max;
max := dim(p,1)-1;
for i from 0 upto max do p[i] := 0 od;
for i from 1 upto max/2 do
for j from i*2 by i upto max do
p[j] := p[j] + i
od
od
corp

/* Find all amicable pairs between 0 and 20,000 */
proc nonrec main() void:
word MAX = 20000;
word i, j;
[MAX] word p;
propdivs(p);

for i from 1 upto MAX-1 do
for j from i+1 upto MAX-1 do
if p[i]=j and p[j]=i then
writeln(i:5, ", ", j:5)
fi
od
od
corp
Output:
  220,   284
1184,  1210
2620,  2924
5020,  5564
6232,  6368
10744, 10856
12285, 14595
17296, 18416

## EasyLang

Translation of: Lua
func sumdivs n .
sum = 1
for d = 2 to sqrt n
if n mod d = 0
sum += d + n div d
.
.
return sum
.
for n = 1 to 20000
m = sumdivs n
if m > n
if sumdivs m = n
print n & " " & m
.
.
.

## EchoLisp

;; using (sum-divisors) from math.lib

(lib 'math)
(define (amicable N)
(define n 0)
(for/list ((m (in-range 2 N)))
(set! n (sum-divisors m))
#:continue (>= n (* 1.5 m))  ;; assume n/m < 1.5
#:continue (<= n m) ;; prevent perfect numbers
#:continue (!= (sum-divisors n) m)
(cons m n)))

(amicable 20000)
→ ((220 . 284) (1184 . 1210) (2620 . 2924) (5020 . 5564) (6232 . 6368) (10744 . 10856) (12285 . 14595) (17296 . 18416))

(amicable 1_000_000) ;; 42 pairs
→ (... (802725 . 863835) (879712 . 901424) (898216 . 980984) (947835 . 1125765) (998104 . 1043096))


## Ela

open monad io number list

divisors n = filter ((0 ==) << (n mod)) [1..(n div 2)]
range = [1 .. 20000]
divs = zip range $map (sum << divisors) range pairs = [(n, m) \\ (n, nd) <- divs, (m, md) <- divs | n < m && nd == m && md == n] do putLn pairs ::: IO Output: [(220,284),(1184,1210),(2620,2924),(5020,5564),(6232,6368),(10744,10856),(12285,14595),(17296,18416)] ## Elena Translation of: C# ELENA 6.x : import extensions; import system'routines; const int N = 20000; extension op { ProperDivisors = Range.new(1,self / 2).filterBy::(n => self.mod(n) == 0); get AmicablePairs() { var divsums := Range .new(0, self + 1) .selectBy::(i => i.ProperDivisors.summarize(Integer.new())) .toArray(); ^ 1.repeatTill(divsums.Length) .filterBy::(i) { var ii := i; var sum := divsums[i]; ^ (i < sum) && (sum < divsums.Length) && (divsums[sum] == i) } .selectBy::(i => new { Item1 = i; Item2 = divsums[i]; }) } } public program() { N.AmicablePairs.forEach::(pair) { console.printLine(pair.Item1, " ", pair.Item2) } } Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  ### Alternative variant using strong-typed closures import extensions; import system'routines'stex; import system'collections; const int N = 20000; extension op : IntNumber { Enumerator<int> ProperDivisors = new Range(1,self / 2).filterBy::(int n => self.mod(n) == 0); get AmicablePairs() { auto divsums := new List<int>( cast Enumerator<int>( new Range(0, self).selectBy::(int i => i.ProperDivisors.summarize(0)))); ^ new Range(0, divsums.Length) .filterBy::(int i) { auto sum := divsums[i]; ^ (i < sum) && (sum < divsums.Length) && (divsums[sum] == i) } .selectBy::(int i => new Tuple<int,int>(i,divsums[i])); } } public program() { N.AmicablePairs.forEach::(var Tuple<int,int> pair) { console.printLine(pair.Item1, " ", pair.Item2) } } ### Alternative variant using yield enumerator import extensions; import system'routines'stex; import system'collections; const int Limit = 20000; singleton ProperDivisors { Enumerator<int> function(int number) = Range.new(1, number / 2).filterBy::(int n => number.mod(n) == 0); } public sealed AmicablePairs { int max; constructor(int max) { this max := max } yieldable Tuple<int, int> next() { List<int> divsums := Range.new(0, max + 1).selectBy::(int i => ProperDivisors(i).summarize(0)); for (int i := 1; i < divsums.Length; i += 1) { int sum := divsums[i]; if(i < sum && sum <= divsums.Length && divsums[sum] == i) {$yield new Tuple<int, int>(i, sum);
}
};

^ nil
}
}

public program()
{
auto e := new AmicablePairs(Limit);
for(auto pair := e.next(); pair != nil)
{
console.printLine(pair.Item1, " ", pair.Item2)
}
}
Output:
220 284
1184 1210
2620 2924
5020 5564
6232 6368
10744 10856
12285 14595
17296 18416


## Elixir

Works with: Elixir version 1.2

With proper_divisors#Elixir in place:

defmodule Proper do
def divisors(1), do: []
def divisors(n), do: [1 | divisors(2,n,:math.sqrt(n))] |> Enum.sort

defp divisors(k,_n,q) when k>q, do: []
defp divisors(k,n,q) when rem(n,k)>0, do: divisors(k+1,n,q)
defp divisors(k,n,q) when k * k == n, do: [k | divisors(k+1,n,q)]
defp divisors(k,n,q)                , do: [k,div(n,k) | divisors(k+1,n,q)]
end

map = Map.new(1..20000, fn n -> {n, Proper.divisors(n) |> Enum.sum} end)
Enum.filter(map, fn {n,sum} -> map[sum] == n and n < sum end)
|> Enum.sort
|> Enum.each(fn {i,j} -> IO.puts "#{i} and #{j}" end)

Output:
220 and 284
1184 and 1210
2620 and 2924
5020 and 5564
6232 and 6368
10744 and 10856
12285 and 14595
17296 and 18416


## Erlang

### Erlang, slow

Very slow solution. Same functions by and large as in proper divisors and co.

-module(properdivs).
-export([amicable/1,divs/1,sumdivs/1]).

amicable(Limit) -> amicable(Limit,[],3,2).

amicable(Limit,List,_Current,Acc) when Acc >= Limit -> List;
amicable(Limit,List,Current,Acc) when Current =< Acc/2  ->
amicable(Limit,List,Acc,Acc+1);
amicable(Limit,List,Current,Acc) ->
CS = sumdivs(Current),
AS = sumdivs(Acc),
if
CS == Acc andalso AS == Current andalso Acc =/= Current ->
io:format("A: ~w, B: ~w, ~nL: ~w~w~n",  [Current,Acc,divs(Current),divs(Acc)]),
NL = List ++ [{Current,Acc}],
amicable(Limit,NL,Acc+1,Acc+1);
true ->
amicable(Limit,List,Current-1,Acc) end.

divs(0) -> [];
divs(1) -> [];
divs(N) -> lists:sort(divisors(1,N)).

divisors(1,N) ->
[1] ++ divisors(2,N,math:sqrt(N)).

divisors(K,_N,Q) when K > Q -> [];
divisors(K,N,_Q) when N rem K =/= 0 ->
[] ++ divisors(K+1,N,math:sqrt(N));
divisors(K,N,_Q) when K * K  == N ->
[K] ++ divisors(K+1,N,math:sqrt(N));
divisors(K,N,_Q) ->
[K, N div K] ++ divisors(K+1,N,math:sqrt(N)).

sumdivs(N) -> lists:sum(divs(N)).

Output:
3> properdivs:amicable(20000).
A: 220, B: 284,
L: [1,2,4,5,10,11,20,22,44,55,110][1,2,4,71,142]
A: 1184, B: 1210,
L: [1,2,4,8,16,32,37,74,148,296,592][1,2,5,10,11,22,55,110,121,242,605]
A: 2620, B: 2924,
L: [1,2,4,5,10,20,131,262,524,655,1310][1,2,4,17,34,43,68,86,172,731,1462]
A: 5020, B: 5564,
L: [1,2,4,5,10,20,251,502,1004,1255,2510][1,2,4,13,26,52,107,214,428,1391,2782]
A: 6232, B: 6368,
L: [1,2,4,8,19,38,41,76,82,152,164,328,779,1558,3116][1,2,4,8,16,32,199,398,796,1592,3184]
A: 10744, B: 10856,
L: [1,2,4,8,17,34,68,79,136,158,316,632,1343,2686,5372][1,2,4,8,23,46,59,92,118,184,236,472,1357,2714,5428]
A: 12285, B: 14595,
L: [1,3,5,7,9,13,15,21,27,35,39,45,63,65,91,105,117,135,189,195,273,315,351,455,585,819,945,1365,1755,2457,4095][1,3,5,7,15,21,35,105,139,417,695,973,2085,2919,4865]
A: 17296, B: 18416,
L: [1,2,4,8,16,23,46,47,92,94,184,188,368,376,752,1081,2162,4324,8648][1,2,4,8,16,1151,2302,4604,9208]
[{220,284},
{1184,1210},
{2620,2924},
{5020,5564},
{6232,6368},
{10744,10856},
{12285,14595},
{17296,18416}]


### Erlang, faster

This is lazy AND depends on the fun fact that we're not really identifying pairs. They just happen to order. Probably, this answer is false in some sense. But a good deal faster :) As above with the additional function.

[See the talk section   amicable pairs, out of order   for this Rosetta Code task.]

friendly(Limit) ->
List = [{X,properdivs:sumdivs(X)} || X <- lists:seq(3,Limit)],
Final = [ X ||
X <- lists:seq(3,Limit),
X == properdivs:sumdivs(proplists:get_value(X,List))
andalso X =/= proplists:get_value(X,List)],
io:format("L: ~w~n", [Final]).

Output:
45> properdivs:friendly(20000).
L: [220,284,1184,1210,2620,2924,5020,5564,6232,6368,10744,10856,12285,14595,17296,18416]
ok


We might answer a challenge by saying:

friendly(Limit) ->
List = [{X,properdivs:sumdivs(X)} || X <- lists:seq(3,Limit)],
Final = [ X || X <- lists:seq(3,Limit), X == properdivs:sumdivs(proplists:get_value(X,List))
andalso X =/= proplists:get_value(X,List)],
findfriendlies(Final,[]).

findfriendlies(List,Acc) when length(List) =< 0 -> Acc;
findfriendlies(List,Acc) ->
A = lists:nth(1,List),
AS = sumdivs(A),
B = lists:nth(2,List),
BS = sumdivs(B),
if
AS == B andalso BS == A ->
{_,BL} = lists:split(2,List),
findfriendlies(BL,Acc++[{A,B}]);
true -> false
end.

Output:
94>  properdivs:friendly(20000).
[{220,284},
{1184,1210},
{2620,2924},
{5020,5564},
{6232,6368},
{10744,10856},
{12285,14595},
{17296,18416}]


In either case, it's a lot faster than the recursion in my first example.

## ERRE

PROGRAM AMICABLE

CONST LIMIT=20000

PROCEDURE SUMPROP(NUM->M)
IF NUM<2 THEN M=0 EXIT PROCEDURE
SUM=1
ROOT=SQR(NUM)
FOR I=2 TO ROOT-1 DO
IF (NUM=I*INT(NUM/I)) THEN
SUM=SUM+I+NUM/I
END IF
IF (NUM=ROOT*INT(NUM/ROOT)) THEN
SUM=SUM+ROOT
END IF
END FOR
M=SUM
END PROCEDURE

BEGIN
PRINT(CHR$(12);) ! CLS PRINT("Amicable pairs < ";LIMIT) FOR N=1 TO LIMIT DO SUMPROP(N->M1) SUMPROP(M1->M2) IF (N=M2 AND N<M1) THEN PRINT(N,M1) END FOR END PROGRAM Output: Amicable pairs < 20000 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  ## F# [2..20000 - 1] |> List.map (fun n-> n, ([1..n/2] |> List.filter (fun x->n % x = 0) |> List.sum)) |> List.map (fun (a,b) ->if a<b then (a,b) else (b,a)) |> List.groupBy id |> List.map snd |> List.filter (List.length >> ((=) 2)) |> List.map List.head |> List.iter (printfn "%A")  Output: (220, 284) (1184, 1210) (2620, 2924) (5020, 5564) (6232, 6368) (10744, 10856) (12285, 14595) (17296, 18416)  ## Factor This solution focuses on the language's namesake: factoring code into small words which are subsequently composed to form more powerful — yet just as simple — words. Using this approach, the final word naturally arrives at the solution. This is often referred to as the bottom-up approach, which is a way in which Factor (and other concatenative languages) commonly differs from other languages. USING: grouping math.primes.factors math.ranges ; : pdivs ( n -- seq ) divisors but-last ; : dsum ( n -- sum ) pdivs sum ; : dsum= ( n m -- ? ) dsum = ; : both-dsum= ( n m -- ? ) [ dsum= ] [ swap dsum= ] 2bi and ; : amicable? ( n m -- ? ) [ both-dsum= ] [ = not ] 2bi and ; : drange ( -- seq ) 2 20000 [a,b) ; : dsums ( -- seq ) drange [ dsum ] map ; : is-am?-seq ( -- seq ) dsums drange [ amicable? ] 2map ; : am-nums ( -- seq ) t is-am?-seq indices ; : am-nums-c ( -- seq ) am-nums [ 2 + ] map ; : am-pairs ( -- seq ) am-nums-c 2 group ; : print-am ( -- ) am-pairs [ >array . ] each ; print-am  Output: { 220 284 } { 1184 1210 } { 2620 2924 } { 5020 5564 } { 6232 6368 } { 10744 10856 } { 12285 14595 } { 17296 18416 }  ## Forth Works with: gforth version 0.7.3 ### Direct approach Calculate many times the divisors. : proper-divisors ( n -- 1..n ) dup 2 / 1+ 1 ?do dup i mod 0= if i swap then loop drop ; : divisors-sum ( 1..n -- n ) dup 1 = if exit then begin over + swap 1 = until ; : pair ( n -- n ) dup 1 = if exit then proper-divisors divisors-sum ; : ?paired ( n -- t | f ) dup pair 2dup pair = >r < r> and ; : amicable-list 1+ 1 do i ?paired if cr i . i pair . then loop ; 20000 amicable-list  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 ok ### Storage approach Use memory to store sum of divisors, a little quicker. variable amicable-table : proper-divisors ( n -- 1..n ) dup 1 = if exit then ( not really but useful ) dup 2 / 1+ 1 ?do dup i mod 0= if i swap then loop drop ; : divisors-sum ( 1..n -- n ) dup 1 = if exit then begin over + swap 1 = until ; : build-amicable-table here amicable-table ! 1+ dup , 1 do i proper-divisors divisors-sum , loop ; : paired cells amicable-table @ + @ ; : .amicables amicable-table @ @ 1 do i paired paired i = i paired i > and if cr i . i paired . then loop ; : amicable-list build-amicable-table .amicables ; 20000 amicable-list  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 ok ## Fortran This version uses some latter-day facilities such as array assignment that could be replaced by an ordinary DO-loop, as could the FOR ALL statement that for two adds two to every second element, for three adds three to every third, etc. Each FORALL statement applies its DO-given increment to all the selected array elements potentially in any order or even simultaneously. Likewise, the "MODULE" protocol could be abandoned, which would mean that the KNOWNSUM array would have to be declared COMMON for access across routines - or the whole re-written as a single mainline. And if the PARAMETER statements were replaced appropriately, this source could be compiled using Fortran 77. Output: Perfect!! 6 Perfect!! 28 Amicable! 220 284 Perfect!! 496 Amicable! 1184 1210 Amicable! 2620 2924 Amicable! 5020 5564 Amicable! 6232 6368 Perfect!! 8128 Amicable! 10744 10856 Amicable! 12285 14595 Amicable! 17296 18416   MODULE FACTORSTUFF !This protocol evades the need for multiple parameters, or COMMON, or one shapeless main line... Concocted by R.N.McLean, MMXV. INTEGER LOTS,ILIMIT !Some bounds. PARAMETER (ILIMIT = 2147483647) !Computer arithmetic is not with real numbers. PARAMETER (LOTS = 22000) !Nor is computer storage infinite. INTEGER KNOWNSUM(LOTS) !Calculate these once as multiple references are expected. CONTAINS !Assistants. INTEGER FUNCTION SUMF(N) !Sum of the proper divisors of N. INTEGER N !The number in question. INTEGER S,F,F2,INC,BOOST !Assistants. IF (N.LE.LOTS) THEN !If we're within reach, SUMF = KNOWNSUM(N) !The result is to hand. ELSE !Otherwise, some on-the-spot effort ensues. Could use SUMF in place of S, but some compilers have been confused by such usage. S = 1 !1 is always a factor of N, but N is deemed not. F = 1 !Prepare a crude search for factors. INC = 1 !One by plodding one. IF (MOD(N,2) .EQ. 1) INC = 2!Ah, but an odd number cannot have an even number as a divisor. 1 F = F + INC !So half the time we can doubleplod. F2 = F*F !Up to F2 < N rather than F < SQRT(N) and worries over inexact arithmetic. IF (F2 .LT. N) THEN !F2 = N handled below. IF (MOD(N,F) .EQ. 0) THEN !Does F divide N? BOOST = F + N/F !Yes. The divisor and its counterpart. IF (S .GT. ILIMIT - BOOST) GO TO 666 !Would their augmentation cause an overflow? S = S + BOOST !No, so count in the two divisors just discovered. END IF !So much for a divisor discovered. GO TO 1 !Try for another. END IF !So much for the horde. IF (F2 .EQ. N) THEN !Special case: N may be a perfect square, not necessarily of a prime number. IF (S .GT. ILIMIT - F) GO TO 666 !It is. And it too might cause overflow. S = S + F !But if not, count F once only. END IF !All done. SUMF = S !This is the result. END IF !Whichever way obtained, RETURN !Done. Cannot calculate the sum, because it exceeds the integer limit. 666 SUMF = -666 !An expression of dismay that the caller will notice. END FUNCTION SUMF !Alternatively, find the prime factors, and combine them... SUBROUTINE PREPARESUMF !Initialise the KNOWNSUM array. Convert the Sieve of Eratoshenes to have each slot contain the sum of the proper divisors of its slot number. Changes to instead count the number of factors, or prime factors, etc. would be simple enough. INTEGER F !A factor for numbers such as 2F, 3F, 4F, 5F, ... KNOWNSUM(1) = 0 !Proper divisors of N do not include N. KNOWNSUM(2:LOTS) = 1 !So, although 1 is a proper divisor of all N, 1 is excluded for itself. DO F = 2,LOTS/2 !Step through all the possible divisors of numbers not exceeding LOTS. FOR ALL(I = F + F:LOTS:F) KNOWNSUM(I) = KNOWNSUM(I) + F !And augment each corresponding slot. END DO !Different divisors can hit the same slot. For instance, 6 by 2 and also by 3. END SUBROUTINE PREPARESUMF !Could alternatively generate all products of prime numbers. END MODULE FACTORSTUFF !Enough assistants. PROGRAM AMICABLE !Seek N such that SumF(SumF(N)) = N, for N up to 20,000. USE FACTORSTUFF !This should help. INTEGER I,N !Steppers. INTEGER S1,S2 !Sums of factors. CALL PREPARESUMF !Values for every N up to the search limit will be called for at least once. c WRITE (6,66) (I,KNOWNSUM(I), I = 1,48) c 66 FORMAT (10(I3,":",I5,"|")) DO N = 2,20000 !Step through the specified search space. S1 = SUMF(N) !Only even numbers appear in the results, but check every one anyway. IF (S1 .EQ. N) THEN !Catch a tight loop. WRITE (6,*) "Perfect!!",N !Self amicable! Would otherwise appear as Amicable! n,n. ELSE IF (S1 .GT. N) THEN !Look for a pair going upwards only. S2 = SUMF(S1) !Since otherwise each would appear twice. IF (S2.EQ.N) WRITE (6,*) "Amicable!",N,S1 !Aha! END IF !So much for that candidate. END DO !On to the next. END !Done.  ## FreeBASIC ### using Mod ' FreeBASIC v1.05.0 win64 Function SumProperDivisors(number As Integer) As Integer If number < 2 Then Return 0 Dim sum As Integer = 0 For i As Integer = 1 To number \ 2 If number Mod i = 0 Then sum += i Next Return sum End Function Dim As Integer n, f Dim As Integer sum(19999) For n = 1 To 19999 sum(n) = SumProperDivisors(n) Next Print "The pairs of amicable numbers below 20,000 are :" Print For n = 1 To 19998 ' f = SumProperDivisors(n) f = sum(n) If f <= n OrElse f < 1 OrElse f > 19999 Then Continue For If f = sum(n) AndAlso n = sum(f) Then Print Using "#####"; n; Print " and "; Using "#####"; sum(n) End If Next Print Print "Press any key to exit the program" Sleep End Output: The pairs of amicable numbers below 20,000 are : 220 and 284 1184 and 1210 2620 and 2924 5020 and 5564 6232 and 6368 10744 and 10856 12285 and 14595 17296 and 18416  ### using "Sieve of Erathosthenes" style ' version 04-10-2016 ' compile with: fbc -s console ' replaced the function with 2 FOR NEXT loops #Define max 20000 ' test for pairs below max #Define max_1 max -1 Dim As String u_str = String(Len(Str(max))+1,"#") Dim As UInteger n, f Dim Shared As UInteger sum(max_1) For n = 2 To max_1 sum(n) = 1 Next For n = 2 To max_1 \ 2 For f = n * 2 To max_1 Step n sum(f) += n Next Next Print Print Using " The pairs of amicable numbers below" & u_str & ", are :"; max Print For n = 1 To max_1 -1 f = Sum(n) If f <= n OrElse f > max Then Continue For If f = sum(n) AndAlso n = sum(f) Then Print Using u_str & " and" & u_str ; n; f End If Next ' empty keyboard buffer While Inkey <> "" : Wend Print : Print : Print " Hit any key to end program" Sleep End  The pairs of amicable numbers below 20,000 are : 220 and 284 1184 and 1210 2620 and 2924 5020 and 5564 6232 and 6368 10744 and 10856 12285 and 14595 17296 and 18416 ## Frink This example uses Frink's built-in efficient factorization algorithms. It can work for arbitrarily large numbers. n = 1 seen = new set do { n = n + 1 if seen.contains[n] next sum = sum[allFactors[n, true, false, false]] if sum != n and sum[allFactors[sum, true, false, false]] == n { println["$n, $sum"] seen.put[sum] } } while n <= 20000 Output: 220, 284 1184, 1210 2620, 2924 5020, 5564 6232, 6368 10744, 10856 12285, 14595 17296, 18416  ## Futhark  This example does not show the output mentioned in the task description on this page (or a page linked to from here). Please ensure that it meets all task requirements and remove this message. Note that phrases in task descriptions such as "print and display" and "print and show" for example, indicate that (reasonable length) output be a part of a language's solution. This program is much too parallel and manifests all the pairs, which requires a giant amount of memory. fun divisors(n: int): []int = filter (fn x => n%x == 0) (map (1+) (iota (n/2))) fun amicable((n: int, nd: int), (m: int, md: int)): bool = n < m && nd == m && md == n fun getPair (divs: [upper](int, int)) (flat_i: int): ((int,int), (int,int)) = let i = flat_i / upper let j = flat_i % upper in unsafe (divs[i], divs[j]) fun main(upper: int): [][2]int = let range = map (1+) (iota upper) let divs = zip range (map (fn n => reduce (+) 0 (divisors n)) range) let amicable = filter amicable (map (getPair divs) (iota (upper*upper))) in map (fn (np,mp) => [#1 np, #1 mp]) amicable  ## FutureBasic local fn Sigma( n as long ) as long long i, root, sum = 1 if n == 1 then exit fn = 0 root = sqr(n) for i = 2 to root if ( n mod i == 0 ) then sum += i + n/i next if root * root == n then sum -= root end fn = sum void local fn CalculateAmicablePairs( limit as long ) long i, m printf @"\nAmicable pairs through %ld are:\n", limit for i = 2 to limit m = fn Sigma(i) if ( m > i ) if ( fn Sigma(m) == i ) then printf @"%6ld and %ld", i, m end if next end fn CFTimeInterval t t = fn CACurrentMediaTime fn CalculateAmicablePairs( 20000 ) printf @"\nCompute time: %.3f ms",(fn CACurrentMediaTime-t)*1000 HandleEvents Output: Amicable pairs through 20000 are: 220 and 284 1184 and 1210 2620 and 2924 5020 and 5564 6232 and 6368 10744 and 10856 12285 and 14595 17296 and 18416 Compute time: 28.701 ms  ## GFA Basic OPENW 1 CLEARW 1 ' DIM f%(20001) ! sum of proper factors for each n FOR i%=1 TO 20000 f%(i%)=@sum_proper_divisors(i%) NEXT i% ' look for pairs FOR i%=1 TO 20000 FOR j%=i%+1 TO 20000 IF f%(i%)=j% AND i%=f%(j%) PRINT "Amicable pair ";i%;" ";j% ENDIF NEXT j% NEXT i% ' PRINT PRINT "-- found all amicable pairs" ~INP(2) CLOSEW 1 ' ' Compute the sum of proper divisors of given number ' FUNCTION sum_proper_divisors(n%) LOCAL i%,sum%,root% ' IF n%>1 ! n% must be 2 or larger sum%=1 ! start with 1 root%=SQR(n%) ! note that root% is an integer ' check possible factors, up to sqrt FOR i%=2 TO root% IF n% MOD i%=0 sum%=sum%+i% ! i% is a factor IF i%*i%<>n% ! check i% is not actual square root of n% sum%=sum%+n%/i% ! so n%/i% will also be a factor ENDIF ENDIF NEXT i% ENDIF RETURN sum% ENDFUNC  Output is: Amicable pair: 220 284 Amicable pair: 1184 1210 Amicable pair: 2620 2924 Amicable pair: 5020 5564 Amicable pair: 6232 6368 Amicable pair: 10744 10856 Amicable pair: 12285 14595 Amicable pair: 17296 18416 -- found all amicable pairs  ## Go package main import "fmt" func pfacSum(i int) int { sum := 0 for p := 1; p <= i/2; p++ { if i%p == 0 { sum += p } } return sum } func main() { var a[20000]int for i := 1; i < 20000; i++ { a[i] = pfacSum(i) } fmt.Println("The amicable pairs below 20,000 are:") for n := 2; n < 19999; n++ { m := a[n] if m > n && m < 20000 && n == a[m] { fmt.Printf(" %5d and %5d\n", n, m) } } }  Output: The amicable pairs below 20,000 are: 220 and 284 1184 and 1210 2620 and 2924 5020 and 5564 6232 and 6368 10744 and 10856 12285 and 14595 17296 and 18416  ## Haskell divisors :: (Integral a) => a -> [a] divisors n = filter ((0 ==) . (n mod)) [1 .. (n div 2)] main :: IO () main = do let range = [1 .. 20000 :: Int] divs = zip range$ map (sum . divisors) range
pairs = [(n, m) | (n, nd) <- divs, (m, md) <- divs,
n < m, nd == m, md == n]
print pairs

Output:
[(220,284),(1184,1210),(2620,2924),(5020,5564),(6232,6368),(10744,10856),(12285,14595),(17296,18416)]

Or, deriving proper divisors above the square root as cofactors (for better performance)

import Data.Bool (bool)

amicablePairsUpTo :: Int -> [(Int, Int)]
amicablePairsUpTo n =
let sigma = sum . properDivisors
in [1 .. n] >>=
(\x ->
let y = sigma x
in bool [] [(x, y)] (x < y && x == sigma y))

properDivisors
:: Integral a
=> a -> [a]
properDivisors n =
let root = (floor . sqrt) (fromIntegral n :: Double)
lows = filter ((0 ==) . rem n) [1 .. root]
in init $lows ++ drop (bool 0 1 (root * root == n)) (reverse (quot n <$> lows))

main :: IO ()
main = mapM_ print $amicablePairsUpTo 20000  Output: (220,284) (1184,1210) (2620,2924) (5020,5564) (6232,6368) (10744,10856) (12285,14595) (17296,18416) ## J factors=: [: /:~@, */&>@{@((^ i.@>:)&.>/)@q:~&__ properDivisors=: factors -. -.&1  (properDivisors is all factors except "the number itself when that number is greater than 1".) Amicable pairs:  1 + ($ #: I.@,) (</~@i.@# * (* |:))(=/ +/@properDivisors@>) 1 + i.20000
220   284
1184  1210
2620  2924
5020  5564
6232  6368
10744 10856
12285 14595
17296 18416


Explanation: We generate sequence of positive integers, starting from 1, and compare each of them to the sum of proper divisors of each of them. Then we fold this comparison diagonally, keeping only the values where the comparison was equal both ways and the smaller value appears before the larger value. Finally, indices into true values give us our amicable pairs.

## Java

Works with: Java version 8
import java.util.Map;
import java.util.function.Function;
import java.util.stream.Collectors;
import java.util.stream.LongStream;

public class AmicablePairs {

public static void main(String[] args) {
int limit = 20_000;

Map<Long, Long> map = LongStream.rangeClosed(1, limit)
.parallel()
.boxed()
.collect(Collectors.toMap(Function.identity(), AmicablePairs::properDivsSum));

LongStream.rangeClosed(1, limit)
.forEach(n -> {
long m = map.get(n);
if (m > n && m <= limit && map.get(m) == n)
System.out.printf("%s %s %n", n, m);
});
}

public static Long properDivsSum(long n) {
return LongStream.rangeClosed(1, (n + 1) / 2).filter(i -> n % i == 0).sum();
}
}

220 284
1184 1210
2620 2924
5020 5564
6232 6368
10744 10856
12285 14595
17296 18416 

## JavaScript

### ES5

(function (max) {

// Proper divisors
function properDivisors(n) {
if (n < 2) return [];
else {
var rRoot = Math.sqrt(n),
intRoot = Math.floor(rRoot),

lows = range(1, intRoot).filter(function (x) {
return (n % x) === 0;
});

return lows.concat(lows.slice(1).map(function (x) {
return n / x;
}).reverse().slice((rRoot === intRoot) | 0));
}
}

// [m..n]
function range(m, n) {
var a = Array(n - m + 1),
i = n + 1;
while (i--) a[i - 1] = i;
return a;
}

// Filter an array of proper divisor sums,
// reading the array index as a function of N (N-1)
// and the sum of proper divisors as a potential M

var pairs = range(1, max).map(function (x) {
return properDivisors(x).reduce(function (a, d) {
return a + d;
}, 0)
}).reduce(function (a, m, i, lst) {
var n = i + 1;

return (m > n) && lst[m - 1] === n ? a.concat([[n, m]]) : a;
}, []);

// [[a]] -> bool -> s -> s
return '{| class="wikitable" ' + (
strStyle ? 'style="' + strStyle + '"' : ''
) + lstRows.map(function (lstRow, iRow) {
var strDelim = ((blnHeaderRow && !iRow) ? '!' : '|');

return '\n|-\n' + strDelim + ' ' + lstRow.map(function (v) {
return typeof v === 'undefined' ? ' ' : v;
}).join(' ' + strDelim + strDelim + ' ');
}).join('') + '\n|}';
}

return wikiTable(
[['N', 'M']].concat(pairs),
true,
'text-align:center'
) + '\n\n' + JSON.stringify(pairs);

})(20000);

Output:
N M
220 284
1184 1210
2620 2924
5020 5564
6232 6368
10744 10856
12285 14595
17296 18416
[[220,284],[1184,1210],[2620,2924],[5020,5564],
[6232,6368],[10744,10856],[12285,14595],[17296,18416]]


### ES6

(() => {
'use strict';

// amicablePairsUpTo :: Int -> [(Int, Int)]
const amicablePairsUpTo = n => {
const sigma = compose(sum, properDivisors);
return enumFromTo(1)(n).flatMap(x => {
const y = sigma(x);
return x < y && x === sigma(y) ? ([
[x, y]
]) : [];
});
};

// properDivisors :: Int -> [Int]
const properDivisors = n => {
const
rRoot = Math.sqrt(n),
intRoot = Math.floor(rRoot),
lows = enumFromTo(1)(intRoot)
.filter(x => 0 === (n % x));
return lows.concat(lows.map(x => n / x)
.reverse()
.slice((rRoot === intRoot) | 0, -1));
};

// TEST -----------------------------------------------

// main :: IO ()
const main = () =>
console.log(unlines(
amicablePairsUpTo(20000).map(JSON.stringify)
));

// GENERIC FUNCTIONS ----------------------------------

// compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
const compose = (...fs) =>
x => fs.reduceRight((a, f) => f(a), x);

// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = m => n =>
Array.from({
length: 1 + n - m
}, (_, i) => m + i);

// sum :: [Num] -> Num
const sum = xs => xs.reduce((a, x) => a + x, 0);

// unlines :: [String] -> String
const unlines = xs => xs.join('\n');

// MAIN ---
return main();
})();

Output:
[220,284]
[1184,1210]
[2620,2924]
[5020,5564]
[6232,6368]
[10744,10856]
[12285,14595]
[17296,18416]

## jq

# unordered
def proper_divisors:
. as $n | if$n > 1 then 1,
(sqrt|floor as $s | range(2;$s+1) as $i | if ($n % $i) == 0 then$i,
(if $i *$i == $n then empty else ($n / $i) end) else empty end) else empty end; def addup(stream): reduce stream as$i (0; . + $i); def task(n): (reduce range(0; n+1) as$n
( [];  . + [$n | addup(proper_divisors)] )) as$listing
| range(1;n+1) as $j | range(1;$j) as $k | if$listing[$j] ==$k and $listing[$k] == \$j
then "k) and \(j) are amicable" else empty end ; task(20000) Output:  jq -c -n -f amicable_pairs.jq 220 and 284 are amicable 1184 and 1210 are amicable 2620 and 2924 are amicable 5020 and 5564 are amicable 6232 and 6368 are amicable 10744 and 10856 are amicable 12285 and 14595 are amicable 17296 and 18416 are amicable  ## Julia Given factor, it is not necessary to calculate the individual divisors to compute their sum. See Abundant, deficient and perfect number classifications for the details. It is safe to exclude primes from consideration; their proper divisor sum is always 1. This code also uses a minor trick to ensure that none of the numbers identified are above the limit. All numbers in the range are checked for an amicable partner, but the pair is cataloged only when the greater member is reached. using Primes, Printf function pcontrib(p::Int64, a::Int64) n = one(p) pcon = one(p) for i in 1:a n *= p pcon += n end return pcon end function divisorsum(n::Int64) dsum = one(n) for (p, a) in factor(n) dsum *= pcontrib(p, a) end dsum -= n end function amicables(L = 2*10^7) acnt = 0 println("Amicable pairs not greater than ", L) for i in 2:L !isprime(i) || continue j = divisorsum(i) j < i && divisorsum(j) == i || continue acnt += 1 println(@sprintf("%4d", acnt), " => ", j, ", ", i) end end amicables()  Output: Note, the output is not ordered by the first figure, see e.g. counters 11, 15, ..., 139, 141, etc. Amicable pairs not greater than 20000000 1 => 220, 284 2 => 1184, 1210 3 => 2620, 2924 4 => 5020, 5564 5 => 6232, 6368 6 => 10744, 10856 7 => 12285, 14595 8 => 17296, 18416 9 => 66928, 66992 10 => 67095, 71145 11 => 63020, 76084 12 => 69615, 87633 13 => 79750, 88730 14 => 122368, 123152 15 => 100485, 124155 16 => 122265, 139815 [...] 138 => 18655744, 19154336 139 => 16871582, 19325698 140 => 17844255, 19895265 141 => 17754165, 19985355  ### Alternative Using the factor() function from the Primes package allows for a quicker calculation, especially when it comes to big numbers. Here we use a busy one-liner with an iterator. The following code prints the amicable pairs in ascending order and also prints the sum of the amicable pair and the cumulative sum of all pairs found so far; this allows to check results, when solving Project Euler problem #21. using Primes function amicable_numbers(max::Integer = 200_000_000) function sum_proper_divisors(n::Integer) sum(vec(map(prod, Iterators.product((p.^(0:m) for (p, m) in factor(n))...)))) - n end count = 0 cumsum = 0 println("count, a, b, a+b, Sum(a+b)") for a in 2:max isprime(a) && continue b = sum_proper_divisors(a) if a < b && sum_proper_divisors(b) == a count += 1 sumab = a + b cumsum += sumab println("count, a, b, sumab, cumsum") end end end amicable_numbers()  Output: count, a, b, a+b, Sum(a+b) 1, 220, 284, 504, 504 2, 1184, 1210, 2394, 2898 3, 2620, 2924, 5544, 8442 4, 5020, 5564, 10584, 19026 5, 6232, 6368, 12600, 31626 6, 10744, 10856, 21600, 53226 7, 12285, 14595, 26880, 80106 8, 17296, 18416, 35712, 115818 9, 63020, 76084, 139104, 254922 10, 66928, 66992, 133920, 388842 11, 67095, 71145, 138240, 527082 12, 69615, 87633, 157248, 684330 13, 79750, 88730, 168480, 852810 14, 100485, 124155, 224640, 1077450 15, 122265, 139815, 262080, 1339530 16, 122368, 123152, 245520, 1585050 [...] 300, 189406984, 203592056, 392999040, 31530421032 301, 190888155, 194594085, 385482240, 31915903272 302, 195857415, 196214265, 392071680, 32307974952 303, 196421715, 224703405, 421125120, 32729100072 304, 199432948, 213484172, 412917120, 33142017192  ## K  propdivs:{1+&0=x!'1+!x%2} (8,2)#v@&{(x=+/propdivs[a])&~x=a:+/propdivs[x]}' v:1+!20000 (220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416)  ## Kotlin // version 1.1 fun sumProperDivisors(n: Int): Int { if (n < 2) return 0 return (1..n / 2).filter{ (n % it) == 0 }.sum() } fun main(args: Array<String>) { val sum = IntArray(20000, { sumProperDivisors(it) } ) println("The pairs of amicable numbers below 20,000 are:\n") for(n in 2..19998) { val m = sum[n] if (m > n && m < 20000 && n == sum[m]) { println(n.toString().padStart(5) + " and " + m.toString().padStart(5)) } } }  Output: The pairs of amicable numbers below 20,000 are: 220 and 284 1184 and 1210 2620 and 2924 5020 and 5564 6232 and 6368 10744 and 10856 12285 and 14595 17296 and 18416  ## Lua Avoids unnecessary divisor sum calculations. Runs in around 0.11 seconds on TIO.RUN. function sumDivs (n) local sum = 1 for d = 2, math.sqrt(n) do if n % d == 0 then sum = sum + d sum = sum + n / d end end return sum end for n = 2, 20000 do m = sumDivs(n) if m > n then if sumDivs(m) == n then print(n, m) end end end  Output:  220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  Alternative version using a table of proper divisors, constructed without division/modulo. Runs is around 0.02 seconds on TIO.RUN. MAX_NUMBER = 20000 sumDivs = {} -- table of proper divisors for i = 1, MAX_NUMBER do sumDivs[ i ] = 1 end for i = 2, MAX_NUMBER do for j = i + i, MAX_NUMBER, i do sumDivs[ j ] = sumDivs[ j ] + i end end for n = 2, MAX_NUMBER do m = sumDivs[n] if m > n then if sumDivs[m] == n then print(n, m) end end end  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  ## MiniScript Translation of: ALGOL W // find amicable pairs p1, p2 where each is equal to the other's proper divisor sum MAX_NUMBER = 20000 pdSum = [1] * ( MAX_NUMBER + 1 ) // table of proper divisors for i in range( 2, MAX_NUMBER ) for j in range( i + i, MAX_NUMBER, i ) pdSum[ j ] += i end for end for // find the amicable pairs up to 20 000 ap = [] for p1 in range( 1, MAX_NUMBER - 1 ) pdSumP1 = pdSum[ p1 ] if pdSumP1 > p1 and pdSumP1 <= MAX_NUMBER and pdSum[ pdSumP1 ] == p1 then print str( p1 ) + " and " + str( pdSumP1 ) + " are an amicable pair" end if end for  Output: 220 and 284 are an amicable pair 1184 and 1210 are an amicable pair 2620 and 2924 are an amicable pair 5020 and 5564 are an amicable pair 6232 and 6368 are an amicable pair 10744 and 10856 are an amicable pair 12285 and 14595 are an amicable pair 17296 and 18416 are an amicable pair  ## MAD  NORMAL MODE IS INTEGER DIMENSION DIVS(20000) PRINT COMMENT  AMICABLE PAIRS R CALCULATE SUM OF DIVISORS OF N INTERNAL FUNCTION(N) ENTRY TO DIVSUM. DS = 0 THROUGH SUMMAT, FOR DIVC=1, 1, DIVC.GE.N SUMMAT WHENEVER N/DIVC*DIVC.E.N, DS = DS+DIVC FUNCTION RETURN DS END OF FUNCTION R CALCULATE SUM OF DIVISORS FOR ALL NUMBERS 1..20000 THROUGH MEMO, FOR I=1, 1, I.GE.20000 MEMO DIVS(I) = DIVSUM.(I) R FIND ALL MATCHING PAIRS THROUGH CHECK, FOR I=1, 1, I.GE.20000 THROUGH CHECK, FOR J=1, 1, J.GE.I CHECK WHENEVER DIVS(I).E.J .AND. DIVS(J).E.I, 0 PRINT FORMAT AMI,I,J VECTOR VALUES AMI = I6,I6* END OF PROGRAM Output: AMICABLE PAIRS 284 220 1210 1184 2924 2620 5564 5020 6368 6232 10856 10744 14595 12285 18416 17296  ## Maple  This example does not show the output mentioned in the task description on this page (or a page linked to from here). Please ensure that it meets all task requirements and remove this message. Note that phrases in task descriptions such as "print and display" and "print and show" for example, indicate that (reasonable length) output be a part of a language's solution. with(NumberTheory): pairs:=[]; for i from 1 to 20000 do for j from i+1 to 20000 do sum1:=SumOfDivisors(j)-j; sum2:=SumOfDivisors(i)-i; if sum1=i and sum2=j and i<>j then pairs:=[op(pairs),[i,j]]; printf("%a", pairs); end if; end do; end do; pairs; ## Mathematica / Wolfram Language amicableQ[n_] := Module[{sum = Total[Most@Divisors@n]}, sum != n && n == Total[Most@Divisors@sum]] Grid@Partition[Cases[Range[4, 20000], _?(amicableQ@# &)], 2]  Output:  220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  ## MATLAB function amicable tic N=2:1:20000; aN=[]; N(isprime(N))=[]; %erase prime numbers I=1; a=N(1); b=sum(pd(a)); while length(N)>1 if a==b %erase perfect numbers; N(N==a)=[]; a=N(1); b=sum(pd(a)); elseif b<a %the first member of an amicable pair is abundant not defective N(N==a)=[]; a=N(1); b=sum(pd(a)); elseif ~ismember(b,N) %the other member was previously erased N(N==a)=[]; a=N(1); b=sum(pd(a)); else c=sum(pd(b)); if a==c aN(I,:)=[I a b]; I=I+1; N(N==b)=[]; else if ~ismember(c,N) %the other member was previously erased N(N==b)=[]; end end N(N==a)=[]; a=N(1); b=sum(pd(a)); clear c end end disp(array2table(aN,'Variablenames',{'N','Amicable1','Amicable2'})) toc end function D=pd(x) K=1:ceil(x/2); D=K(~(rem(x, K))); end  Output:  N Amicable1 Amicable2 _ _________ _________ 1 220 284 2 1184 1210 3 2620 2924 4 5020 5564 5 6232 6368 6 10744 10856 7 12285 14595 8 17296 18416 Elapsed time is 8.958720 seconds.  ## Nim Being a novice, I submitted my code to the Nim community for review and received much feedback and advice. They were instrumental in fine-tuning this code for style and readability, I can't thank them enough. from math import sqrt const N = 524_000_000.int32 proc sumProperDivisors(someNum: int32, chk4less: bool): int32 = result = 1 let maxPD = sqrt(someNum.float).int32 let offset = someNum mod 2 for divNum in countup(2 + offset, maxPD, 1 + offset): if someNum mod divNum == 0: result += divNum + someNum div divNum if chk4less and result >= someNum: return 0 for n in countdown(N, 2): let m = sumProperDivisors(n, true) if m != 0 and n == sumProperDivisors(m, false): echo n, " ", m  Output: 523679536 509379344 511419856 491373104 514823985 475838415 ...... ...... ..... ..... 18416 17296 14595 12285 10856 10744 6368 6232 5564 5020 2924 2620 1210 1184 284 220  Total number of pairs is 442, on my machine the code takes ~389 minutes to run. Here's a second version that uses a large amount of memory but runs in 2m32seconds. Again, thanks to the Nim community from math import sqrt const N = 524_000_000.int32 var x = newSeq[int32](N+1) for i in 2..sqrt(N.float).int32: var p = i*i x[p] += i var j = i + i while (p += i; p <= N): j.inc x[p] += j for m in 4..N: let n = x[m] + 1 if n < m and n != 0 and m == x[n] + 1: echo n, " ", m  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 ..... ..... ...... ...... 426191535 514780497 475838415 514823985 509379344 523679536  ## Oberon-2 MODULE AmicablePairs; IMPORT Out; CONST max = 20000; VAR i,j: INTEGER; pd: ARRAY max + 1 OF LONGINT; PROCEDURE ProperDivisorsSum(n: LONGINT): LONGINT; VAR i,sum: LONGINT; BEGIN sum := 0; IF n > 1 THEN INC(sum,1);i := 2; WHILE (i < n) DO IF (n MOD i) = 0 THEN INC(sum,i) END; INC(i) END END; RETURN sum END ProperDivisorsSum; BEGIN FOR i := 0 TO max DO pd[i] := ProperDivisorsSum(i) END; FOR i := 2 TO max DO FOR j := i + 1 TO max DO IF (pd[i] = j) & (pd[j] = i) THEN Out.Char('[');Out.Int(i,0);Out.Char(',');Out.Int(j,0);Out.Char("]");Out.Ln END END END END AmicablePairs. Output: [220,284] [1184,1210] [2620,2924] [5020,5564] [6232,6368] [10744,10856] [12285,14595] [17296,18416]  ## Oforth Using properDivs implementation tasks without optimization (calculating proper divisors sum without returning a list for instance) : import: mapping Integer method: properDivs -- [] #[ self swap mod 0 == ] self 2 / seq filter ; : amicables | i j | Array new 20000 loop: i [ i properDivs sum dup ->j i <= if continue then j properDivs sum i <> if continue then [ i, j ] over add ] ; Output: amicables . [[220, 284], [1184, 1210], [2620, 2924], [5020, 5564], [6232, 6368], [10744, 10856], [12285, 14595], [17296, 18416]]  ## OCaml let rec isqrt n = if n = 1 then 1 else let _n = isqrt (n - 1) in (_n + (n / _n)) / 2 let sum_divs n = let sum = ref 1 in for d = 2 to isqrt n do if (n mod d) = 0 then sum := !sum + (n / d + d); done; !sum let () = for n = 2 to 20000 do let m = sum_divs n in if (m > n) then if (sum_divs m) = n then Printf.printf "%d %d\n" n m; done  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 ## PARI/GP for(x=1,20000,my(y=sigma(x)-x); if(y>x && x == sigma(y)-y,print(x" "y))) Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 ## Pascal ### Direct approach Works with: Turbo Pascal Works with: Free Pascal This version mutates the Sieve of Eratoshenes from striking out factors into summing factors. The Pascal source compiles with Turbo Pascal (7, patched to avoid the zero divide problem for cpu speeds better than ~150MHz) except that the array limit is too large: 15,000 works but does not reach 20,000. The Free Pascal compiler however can handle an array of 20,000 elements. Because the sum of factors of N can exceed N an ad-hoc SumF procedure is provided, thus the search could continue past the table limit, but at a cost in calculation time. Output is Chasing Chains of Sums of Factors of Numbers. Perfect!! 6, Perfect!! 28, Amicable! 220,284, Perfect!! 496, Amicable! 1184,1210, Amicable! 2620,2924, Amicable! 5020,5564, Amicable! 6232,6368, Perfect!! 8128, Amicable! 10744,10856, Amicable! 12285,14595, Sociable: 12496,14288,15472,14536,14264, Sociable: 14316,19116,31704,47616,83328,177792,295488,629072,589786,294896,358336,418904,366556,274924,275444,243760,376736,381028,285778,152990,122410,97946,48976,45946,22976,22744,19916,17716, Amicable! 17296,18416,  Source file:  Program SumOfFactors; uses crt; {Perpetrated by R.N.McLean, December MCMXCV} //{DEFINE ShowOverflow} {IFDEF FPC} {MODE DELPHI}//tested with lots = 524*1000*1000 takes 75 secs generating KnownSum {ENDIF} var outf: text; const Limit = 2147483647; const lots = 20000; {This should be much bigger, but problems apply.} var KnownSum: array[1..lots] of longint; Function SumF(N: Longint): Longint; var f,f2,s,ulp: longint; Begin if n <= lots then SumF:=KnownSum[N] {Hurrah!} else begin {This is really crude...} s:=1; {1 is always a factor, but N is not.} f:=2; f2:=f*f; while f2 < N do begin if N mod f = 0 then begin {We have a divisor, and its friend.} ulp:=f + (N div f); if s > Limit - ulp then begin SumF:=-666; exit; end; s:=s + ulp; end; f:=f + 1; f2:=f*f; end; if f2 = N then {A perfect square gets its factor in once only.} if s <= Limit - f then s:=s + f else begin SumF:=-667; exit; end; SumF:=s; end; End; var i,j,l,sf,fs: LongInt; const enuff = 666; {Only so much sociability.} var trail: array[0..enuff] of longint; BEGIN ClrScr; WriteLn('Chasing Chains of Sums of Factors of Numbers.'); for i:=1 to lots do KnownSum[i]:=1; {Sigh. KnownSum:=1;} {start summing every divisor } for i:=2 to lots do begin j:=i + i; While j <= lots do {Sigh. For j:=i + i:Lots:i do KnownSum[j]:=KnownSum[j] + i;} begin KnownSum[j]:=KnownSum[j] + i; j:=j + i; end; end; {Enough preparation.} Assign(outf,'Factors.txt'); ReWrite(Outf); WriteLn(Outf,'Chasing Chains of Sums of Factors of Numbers.'); for i:=2 to lots do {Search.} begin l:=0; sf:=SumF(i); while (sf > i) and (l < enuff) do begin l:=l + 1; trail[l]:=sf; sf:=SumF(sf); end; if l >= enuff then writeln('Rope ran out! ',i); {IFDEF ShowOverflow} if sf < 0 then writeln('Overflow with ',i); {ENDIF} if i = sf then {A loop?} begin {Yes. Reveal its members.} trail[0]:=i; {The first.} if l = 0 then write('Perfect!! ') else if l = 1 then write('Amicable! ') else write('Sociable: '); for j:=0 to l do Write(Trail[j],','); WriteLn; if l = 0 then write(outf,'Perfect!! ') else if l = 1 then write(outf,'Amicable! ') else write(outf,'Sociable: '); for j:=0 to l do write(outf,Trail[j],','); WriteLn(outf); end; end; Close (outf); END.  ### More expansive. a "normal" Version. Nearly fast as perl using nTheory. program AmicablePairs; {IFDEF FPC} {MODE DELPHI} {H+} {ELSE} {APPTYPE CONSOLE} {ENDIF} uses sysutils; const MAX = 20000; //MAX = 20*1000*1000; type tValue = LongWord; tpValue = ^tValue; tPower = array[0..31] of tValue; tIndex = record idxI, idxS : Uint64; end; var Indices : array[0..511] of tIndex; //primes up to 65536 enough until 2^32 primes : array[0..6542] of tValue; procedure InitPrimes; // sieve of erathosthenes without multiples of 2 type tSieve = array[0..(65536-1) div 2] of ansichar; var ESieve : ^tSieve; idx,i,j,p : LongINt; Begin new(ESieve); fillchar(ESieve^[0],SizeOF(tSieve),#1); primes[0] := 2; idx := 1; //sieving j := 1; p := 2*j+1; repeat if Esieve^[j] = #1 then begin i := (2*j+2)*j;// i := (sqr(p) -1) div 2; if i > High(tSieve) then BREAK; repeat ESIeve^[i] := #0; inc(i,p); until i > High(tSieve); end; inc(j); inc(p,2); until j >High(tSieve); //collecting For i := 1 to High(tSieve) do IF Esieve^[i] = #1 then Begin primes[idx] := 2*i+1; inc(idx); IF idx>High(primes) then BREAK; end; dispose(Esieve); end; procedure Su_append(n,factor:tValue;var su:string); var q,p : tValue; begin p := 0; repeat q := n div factor; IF q*factor<>n then Break; inc(p); n := q; until false; IF p > 0 then IF p= 1 then su:= su+IntToStr(factor)+'*' else su:= su+IntToStr(factor)+'^'+IntToStr(p)+'*'; end; procedure ProperDivs(n: Uint64); //output of prime factorization var su : string; primNo : tValue; p:tValue; begin str(n:8,su); su:= su +' ['; primNo := 0; p := primes[0]; repeat Su_Append(n,p,su); inc(primNo); p := primes[primNo]; until (p=0) OR (p*p >= n); p := n; Su_Append(n,p,su); su[length(su)] := ']'; writeln(su); end; procedure AmPairOutput(cnt:tValue); var i : tValue; r_max,r_min,r : double; begin r_max := 1.0; r_min := 16.0; For i := 0 to cnt-1 do with Indices[i] do begin r := IdxS/IDxI; writeln(i+1:4,IdxI:16,IDxS:16,' ratio ',r:10:7); IF r < 1 then begin writeln(i); readln; halt; end; if r_max < r then r_max := r else if r_min > r then r_min := r; IF cnt < 20 then begin ProperDivs(IdxI); ProperDivs(IdxS); end; end; writeln(' min ratio ',r_min:12:10); writeln(' max ratio ',r_max:12:10); end; procedure SumOFProperDiv(n: tValue;var SumOfProperDivs:tValue); // calculated by prime factorization var i,q, primNo, Prime,pot : tValue; SumOfDivs: tValue; begin i := N; SumOfDivs := 1; primNo := 0; Prime := Primes[0]; q := i DIV Prime; repeat if q*Prime = i then Begin pot := 1; repeat i := q; q := i div Prime; Pot := Pot * Prime+1; until q*Prime <> i; SumOfDivs := SumOfDivs * pot; end; Inc(primNo); Prime := Primes[primNo]; q := i DIV Prime; {check if i already prime} if Prime > q then begin prime := i; q := 1; end; until i = 1; SumOfProperDivs := SumOfDivs - N; end; function Check:tValue; const //going backwards DIV23 : array[0..5] of byte = //== 5,4,3,2,1,0 (1,0,0,0,1,0); var i,s,k,n : tValue; idx : nativeInt; begin n := 0; idx := 3; For i := 2 to MAX do begin //must be divisble by 2 or 3 ( n < High(tValue) < 1e14 ) IF DIV23[idx] = 0 then begin SumOFProperDiv(i,s); //only 24.7...% IF s>i then Begin SumOFProperDiv(s,k); IF k = i then begin With indices[n] do begin idxI := i; idxS := s; end; inc(n); end; end; end; dec(idx); IF idx < 0 then idx := high(DIV23); end; result := n; end; var T2,T1: TDatetime; APcnt: tValue; begin InitPrimes; T1:= time; APCnt:= Check; T2:= time; AmPairOutput(APCnt); writeln('Time to find amicable pairs ',FormatDateTime('HH:NN:SS.ZZZ' ,T2-T1)); {IFNDEF UNIX} readln;{ENDIF} end.  Output  1 220 284 ratio 1.2909091 220 [2^2*5*11*220] 284 [2^2*284] 2 1184 1210 ratio 1.0219595 1184 [2^5*1184] 1210 [2*5*11^2*1210] 3 2620 2924 ratio 1.1160305 2620 [2^2*5*2620] 2924 [2^2*17*43*2924] 4 5020 5564 ratio 1.1083665 5020 [2^2*5*5020] 5564 [2^2*13*5564] 5 6232 6368 ratio 1.0218228 6232 [2^3*19*41*6232] 6368 [2^5*6368] 6 10744 10856 ratio 1.0104244 10744 [2^3*17*79*10744] 10856 [2^3*23*59*10856] 7 12285 14595 ratio 1.1880342 12285 [3^3*5*7*13*12285] 14595 [3*5*7*14595] 8 17296 18416 ratio 1.0647549 17296 [2^4*23*47*17296] 18416 [2^4*18416] ### Alternative about 25-times faster. This will not output the amicable number unless both! numbers are under the given limit. So there will be differences to "Table of n, a(n) for n=1..39374" https://oeis.org/A002025/b002025.txt Up to 524'000'000 the pairs found are only correct by number up to no. 437 460122410 and only 442 out of 455 are found, because some pairs exceed the limit. The limits of the ratio between the numbers of the amicable pair up to 1E14 are, based on b002025.txt: No. lower upper 31447 52326552030976 52326637800704 ratio 1.0000016 52326552030976 [2^8*563*6079*59723] 52326637800704 [2^8*797*1439*178223] 38336 92371445691525 154378742017851 ratio 1.6712821 92371445691525 [3^2*5^2*7^2*11*13^2*23*29^2*233] 154378742017851 [3^2*13^2*53*337*5682671]  The distance check is being corrected, the lower number is now not limited. The used method is not useful for very high limits. n = p[1]^a[1]*p[2]^a[2]*...p[l]^a[l] sum of divisors(n) = s(n) = (p[1]^(a[1]+1) -1) / (p[1] -1) * ... * (p[l]^(a[l]+1) -1) / (p[l] -1) with p[k]^(a[k]+1) -1) / (p[k] -1) = sum (i= [1..a[k]])(p[k]^i) Using "Sieve of Erathosthenes"-style program AmicPair; {find amicable pairs in a limited region 2..MAX beware that >both< numbers must be smaller than MAX there are 455 amicable pairs up to 524*1000*1000 correct up to #437 460122410 } //optimized for freepascal 2.6.4 32-Bit {IFDEF FPC} {MODE DELPHI} {OPTIMIZATION ON,peephole,cse,asmcse,regvar} {CODEALIGN loop=1,proc=8} {ELSE} {APPTYPE CONSOLE} {ENDIF} uses sysutils; type tValue = LongWord; tpValue = ^tValue; tDivSum = array[0..0] of tValue;// evil, but dynamic arrays are slower tpDivSum = ^tDivSum; tPower = array[0..31] of tValue; tIndex = record idxI, idxS : tValue; end; var power, PowerFac : tPower; ds : array of tValue; Indices : array[0..511] of tIndex; DivSumField : tpDivSum; MAX : tValue; procedure Init; var i : LongInt; begin DivSumField[0]:= 0; For i := 1 to MAX do DivSumField[i]:= 1; end; procedure ProperDivs(n: tValue); //Only for output, normally a factorication would do var su,so : string; i,q : tValue; begin su:= '1'; so:= ''; i := 2; while i*i <= n do begin q := n div i; IF q*i -n = 0 then begin su:= su+','+IntToStr(i); IF q <> i then so:= ','+IntToStr(q)+so; end; inc(i); end; writeln(' [',su+so,']'); end; procedure AmPairOutput(cnt:tValue); var i : tValue; r : double; begin r := 1.0; For i := 0 to cnt-1 do with Indices[i] do begin writeln(i+1:4,IdxI:12,IDxS:12,' ratio ',IdxS/IDxI:10:7); if r < IdxS/IDxI then r := IdxS/IDxI; IF cnt < 20 then begin ProperDivs(IdxI); ProperDivs(IdxS); end; end; writeln(' max ratio ',r:10:4); end; function Check:tValue; var i,s,n : tValue; begin n := 0; For i := 1 to MAX do begin //s = sum of proper divs (I) == sum of divs (I) - I s := DivSumField^[i]; IF (s <=MAX) AND (s>i) AND (DivSumField^[s]= i)then begin With indices[n] do begin idxI := i; idxS := s; end; inc(n); end; end; result := n; end; Procedure CalcPotfactor(prim:tValue); //PowerFac[k] = (prim^(k+1)-1)/(prim-1) == Sum (i=0..k) prim^i var k: tValue; Pot, //== prim^k PFac : Int64; begin Pot := prim; PFac := 1; For k := 0 to High(PowerFac) do begin PFac := PFac+Pot; IF (POT > MAX) then BREAK; PowerFac[k] := PFac; Pot := Pot*prim; end; end; procedure InitPW(prim:tValue); begin fillchar(power,SizeOf(power),#0); CalcPotfactor(prim); end; function NextPotCnt(p: tValue):tValue; //return the first power <> 0 //power == n to base prim var i : tValue; begin result := 0; repeat i := power[result]; Inc(i); IF i < p then BREAK else begin i := 0; power[result] := 0; inc(result); end; until false; power[result] := i; end; procedure Sieve(prim: tValue); var actNumber,idx : tValue; begin //sieve with "small" primes while prim*prim <= MAX do begin InitPW(prim); Begin //actNumber = actual number = n*prim actNumber := prim; idx := prim; while actNumber <= MAX do begin dec(idx); IF idx > 0 then DivSumField^[actNumber] *= PowerFac[0] else Begin DivSumField^[actNumber] *= PowerFac[NextPotCnt(prim)+1]; idx := Prim; end; inc(actNumber,prim); end; end; //next prime repeat inc(prim); until DivSumField^[prim]= 1;//(DivSumField[prim] = 1); end; //sieve with "big" primes, only one factor is possible while 2*prim <= MAX do begin InitPW(prim); Begin actNumber := prim; idx := PowerFac[0]; while actNumber <= MAX do begin DivSumField^[actNumber] *= idx; inc(actNumber,prim); end; end; repeat inc(prim); until DivSumField^[prim]= 1; end; For idx := 2 to MAX do dec(DivSumField^[idx],idx); end; var T2,T1,T0: TDatetime; APcnt: tValue; i: NativeInt; begin MAX := 20000; IF ParamCount > 0 then MAX := StrToInt(ParamStr(1)); setlength(ds,MAX); DivSumField := @ds[0]; T0:= time; For i := 1 to 1 do Begin Init; Sieve(2); end; T1:= time; APCnt := Check; T2:= time; AmPairOutput(APCnt); writeln(APCnt,' amicable pairs til ',MAX); writeln('Time to calc sum of divs ',FormatDateTime('HH:NN:SS.ZZZ' ,T1-T0)); writeln('Time to find amicable pairs ',FormatDateTime('HH:NN:SS.ZZZ' ,T2-T1)); setlength(ds,0); {IFNDEF UNIX} readln; {ENDIF} end.  output  220 284 [1,2,4,5,10,11,20,22,44,55,110] [1,2,4,71,142] 1184 1210 [1,2,4,8,16,32,37,74,148,296,592] [1,2,5,10,11,22,55,110,121,242,605] 2620 2924 [1,2,4,5,10,20,131,262,524,655,1310] [1,2,4,17,34,43,68,86,172,731,1462] 5020 5564 [1,2,4,5,10,20,251,502,1004,1255,2510] [1,2,4,13,26,52,107,214,428,1391,2782] 6232 6368 [1,2,4,8,19,38,41,76,82,152,164,328,779,1558,3116] [1,2,4,8,16,32,199,398,796,1592,3184] 10744 10856 [1,2,4,8,17,34,68,79,136,158,316,632,1343,2686,5372] [1,2,4,8,23,46,59,92,118,184,236,472,1357,2714,5428] 12285 14595 [1,3,5,7,9,13,15,21,27,35,39,45,63,65,91,105,117,135,189,195,273,315,351,455,585,819,945,1365,1755,2457,4095] [1,3,5,7,15,21,35,105,139,417,695,973,2085,2919,4865] 17296 18416 [1,2,4,8,16,23,46,47,92,94,184,188,368,376,752,1081,2162,4324,8648] [1,2,4,8,16,1151,2302,4604,9208] 8 amicable numbers up to 20000 00:00:00.000 .... Test with 524*1000*1000 Linux32, FPC 3.0.1, i4330 3.5 Ghz //Win32 swaps first to allocate 2 GB ) 440 475838415 514823985 ratio 1.0819303 441 491373104 511419856 ratio 1.0407974 442 509379344 523679536 ratio 1.0280738 max ratio 1.3537 442 amicable pairs til 524000000 Time to calc sum of divs 00:00:12.601 Time to find amicable pairs 00:00:02.557  ## Perl Not particularly clever, but instant for this example, and does up to 20 million in 11 seconds. Library: ntheory use ntheory qw/divisor_sum/; for my x (1..20000) { my y = divisor_sum(x)-x; say "x y" if y > x && x == divisor_sum(y)-y; }  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 ## Phix with javascript_semantics for m=1 to 20000 do integer n = sum(factors(m,-1)) if m<n and m=sum(factors(n,-1)) then ?{m,n} end if end for  Output: {220,284} {1184,1210} {2620,2924} {5020,5564} {6232,6368} {10744,10856} {12285,14595} {17296,18416}  ## Phixmonti def sumDivs var n 1 var sum n sqrt 2 swap 2 tolist for var d n d mod not if sum d + n d / + var sum endif endfor sum enddef 2 20000 2 tolist for var i i sumDivs var m m i > if m sumDivs i == if i print "\t" print m print nl endif endif endfor nl msec print " s" print ## PHP <?php function sumDivs (n) { sum = 1; for (d = 2; d <= sqrt(n); d++) { if (n % d == 0) sum += n / d + d; } return sum; } for (n = 2; n < 20000; n++) { m = sumDivs(n); if (m > n) { if (sumDivs(m) == n) echo n."&ensp;".m."<br />"; } } ?>  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 ## Picat Different approaches to solve this task:  * foreach loop (two variants) * list comprehension * while loop.  Also, the calculation of the sum of divisors is tabled (the table is cleared between each run). go => N = 20000, println(amicable1), time(amicable1(N)), % initialize_table is needed to clear the table cache % of sum_divisors/1 between each run. initialize_table, println(amicable2), time(amicable2(N)), initialize_table, println(amicable3), time(amicable3(N)), initialize_table, println(amicable4), time(amicable4(N)), nl. % Foreach loop and a map (hash table) amicable1(N) => Pairs = new_map(), foreach(A in 1..N) B = sum_divisors(A), C = sum_divisors(B), if A != B, A == C then Pairs.put([A,B].sort(),1) end end, println(Pairs.keys().sort()). % List comprehension amicable2(N) => println([[A,B].sort() : A in 1..N, B = sum_divisors(A), C = sum_divisors(B), A != B, A == C].remove_dups()). % While loop amicable3(N) => A = 1, while(A <= N) B = sum_divisors(A), if A < B, A == sum_divisors(B) then print([A,B]), print(" ") end, A := A + 1 end, nl. % Foreach loop, everything in the condition amicable4(N) => foreach(A in 1..N, B = sum_divisors(A), A < B, A == sum_divisors(B)) print([A,B]), print(" ") end, nl. % % Sum of divisors of N % table sum_divisors(N) = Sum => sum_divisors(2,N,1,Sum). % Base case: exceeding the limit sum_divisors(I,N,Sum0,Sum), I > floor(sqrt(N)) => Sum = Sum0. % I is a divisor of N sum_divisors(I,N,Sum0,Sum), N mod I == 0 => Sum1 = Sum0 + I, (I != N div I -> Sum2 = Sum1 + N div I ; Sum2 = Sum1 ), sum_divisors(I+1,N,Sum2,Sum). % I is not a divisor of N. sum_divisors(I,N,Sum0,Sum) => sum_divisors(I+1,N,Sum0,Sum). Output: amicable1 [[220,284],[1184,1210],[2620,2924],[5020,5564],[6232,6368],[10744,10856],[12285,14595],[17296,18416]] CPU time 0.114 seconds. amicable2 [[220,284],[1184,1210],[2620,2924],[5020,5564],[6232,6368],[10744,10856],[12285,14595],[17296,18416]] CPU time 0.106 seconds. amicable3 [220,284] [1184,1210] [2620,2924] [5020,5564] [6232,6368] [10744,10856] [12285,14595] [17296,18416] CPU time 0.111 seconds. amicable4 [220,284] [1184,1210] [2620,2924] [5020,5564] [6232,6368] [10744,10856] [12285,14595] [17296,18416] CPU time 0.107 seconds.  ## PicoLisp (de accud (Var Key) (if (assoc Key (val Var)) (con @ (inc (cdr @))) (push Var (cons Key 1)) ) Key ) (de **sum (L) (let S 1 (for I (cdr L) (inc 'S (** (car L) I)) ) S ) ) (de factor-sum (N) (if (=1 N) 0 (let (R NIL D 2 L (1 2 2 . (4 2 4 2 4 6 2 6 .)) M (sqrt N) N1 N S 1 ) (while (>= M D) (if (=0 (% N1 D)) (setq M (sqrt (setq N1 (/ N1 (accud 'R D)))) ) (inc 'D (pop 'L)) ) ) (accud 'R N1) (for I R (setq S (* S (**sum I))) ) (- S N) ) ) ) (bench (for I 20000 (let X (factor-sum I) (and (< I X) (= I (factor-sum X)) (println I X) ) ) ) ) Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 0.101 sec  ## PL/I Translation of: REXX *process source xref; ami: Proc Options(main); p9a=time(); Dcl (p9a,p9b,p9c) Pic'(9)9'; Dcl sumpd(20000) Bin Fixed(31); Dcl pd(300) Bin Fixed(31); Dcl npd Bin Fixed(31); Dcl (x,y) Bin Fixed(31); Do x=1 To 20000; Call proper_divisors(x,pd,npd); sumpd(x)=sum(pd,npd); End; p9b=time(); Put Edit('sum(pd) computed in',(p9b-p9a)/1000,' seconds elapsed') (Skip,col(7),a,f(6,3),a); Do x=1 To 20000; Do y=x+1 To 20000; If y=sumpd(x) & x=sumpd(y) Then Put Edit(x,y,' found after ',elapsed(),' seconds') (Skip,2(f(6)),a,f(6,3),a); End; End; Put Edit(elapsed(),' seconds total search time')(Skip,f(6,3),a); proper_divisors: Proc(n,pd,npd); Dcl (n,pd(300),npd) Bin Fixed(31); Dcl (d,delta) Bin Fixed(31); npd=0; If n>1 Then Do; If mod(n,2)=1 Then /* odd number */ delta=2; Else /* even number */ delta=1; Do d=1 To n/2 By delta; If mod(n,d)=0 Then Do; npd+=1; pd(npd)=d; End; End; End; End; sum: Proc(pd,npd) Returns(Bin Fixed(31)); Dcl (pd(300),npd) Bin Fixed(31); Dcl sum Bin Fixed(31) Init(0); Dcl i Bin Fixed(31); Do i=1 To npd; sum+=pd(i); End; Return(sum); End; elapsed: Proc Returns(Dec Fixed(6,3)); p9c=time(); Return((p9c-p9b)/1000); End; End; Output:  sum(pd) computed in 0.510 seconds elapsed 220 284 found after 0.010 seconds 1184 1210 found after 0.060 seconds 2620 2924 found after 0.110 seconds 5020 5564 found after 0.210 seconds 6232 6368 found after 0.260 seconds 10744 10856 found after 2.110 seconds 12285 14595 found after 2.150 seconds 17296 18416 found after 2.240 seconds 2.250 seconds total search time ### PL/I-80 #### Computing the divisor sum on the fly Rather than populating an array with the sum of the proper divisors and then searching, the approach here calculates them on the fly as needed, saving memory, and avoiding a noticeable lag on program startup on the ancient systems that hosted PL/I-80. amicable: procedure options (main); %replace search_limit by 20000; dcl (a, b, found) fixed bin; put skip list ('Searching for amicable pairs up to '); put edit (search_limit) (f(5)); found = 0; do a = 2 to search_limit; b = sumf(a); if (b > a) then do; if (sumf(b) = a) then do; found = found + 1; put skip edit (a,b) (f(7)); end; end; end; put skip list (found, ' pairs were found'); stop; /* return sum of the proper divisors of n */ sumf: procedure(n) returns (fixed bin); dcl (n, sum, f1, f2) fixed bin; sum = 1; /* 1 is a proper divisor of every number */ f1 = 2; do while ((f1 * f1) < n); if mod(n, f1) = 0 then do; sum = sum + f1; f2 = n / f1; /* don't double count identical co-factors! */ if f2 > f1 then sum = sum + f2; end; f1 = f1 + 1; end; return (sum); end sumf; end amicable; Output: Searching for amicable pairs up to 20000 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 8 pairs were found  #### Without using division/modulo amicable: procedure options (main); %replace search_limit by 20000; dcl sumf( 1 : search_limit ) fixed bin; dcl (a, b, found) fixed bin; put skip list ('Searching for amicable pairs up to '); put edit (search_limit) (f(5)); do a = 1 to search_limit; sumf( a ) = 1; end; do a = 2 to search_limit; do b = a + a to search_limit by a; sumf( b ) = sumf( b ) + a; end; end; found = 0; do a = 2 to search_limit; b = sumf(a); if (b > a) then do; if (sumf(b) = a) then do; found = found + 1; put skip edit (a,b) (f(7)); end; end; end; put skip list (found, ' pairs were found'); stop; end amicable; Output: Same as the other PLI-80 sample. ## PL/M 100H: /* CP/M CALLS */ BDOS: PROCEDURE (FN, ARG); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS; EXIT: PROCEDURE; CALL BDOS(0,0); END EXIT; PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9,S); END PRINT; /* PRINT A NUMBER */ PRINTNUMBER: PROCEDURE (N); DECLARE S (6) BYTE INITIAL ('.....'); DECLARE (N, P) ADDRESS, C BASED P BYTE; P = .S(5); DIGIT: P = P - 1; C = N MOD 10 + '0'; N = N / 10; IF N > 0 THEN GO TO DIGIT; CALL PRINT(P); END PRINTNUMBER; /* CALCULATE SUMS OF PROPER DIVISORS */ DECLARE DIVSUM (20001) ADDRESS; DECLARE (I, J) ADDRESS; DO I=2 TO 20000; DIVSUM(I) = 1; END; DO I=2 TO 10000; DO J = I*2 TO 20000 BY I; DIVSUM(J) = DIVSUM(J) + I; END; END; /* TEST EACH PAIR */ DO I=2 TO 20000; J = DIVSUM(I); IF J > I AND J <= 20000 THEN DO; IF DIVSUM(J) = I THEN DO; CALL PRINTNUMBER(I); CALL PRINT(.', '); CALL PRINTNUMBER(J); CALL PRINT(.(13,10,'')); END; END; END; CALL EXIT; EOF Output: 220, 284 1184, 1210 2620, 2924 5020, 5564 6232, 6368 10744, 10856 12285, 14595 17296, 18416 ## PowerShell Works with: PowerShell version 2 function Get-ProperDivisorSum ( [int]N ) { Sum = 1 If ( N -gt 3 ) { SqrtN = [math]::Sqrt( N ) ForEach ( Divisor1 in 2..SqrtN ) { Divisor2 = N / Divisor1 If ( Divisor2 -is [int] ) { Sum += Divisor1 + Divisor2 } } If ( SqrtN -is [int] ) { Sum -= SqrtN } } return Sum } function Get-AmicablePairs ( N = 300 ) { ForEach ( X in 1..N ) { Sum = Get-ProperDivisorSum X If ( Sum -gt X -and X -eq ( Get-ProperDivisorSum Sum ) ) { "X, Sum" } } } Get-AmicablePairs 20000  Output: 220, 284 1184, 1210 2620, 2924 5020, 5564 6232, 6368 10744, 10856 12285, 14595 17296, 18416  ## Prolog Works with: SWI-Prolog 7 With some guidance from other solutions here: divisor(N, Divisor) :- UpperBound is round(sqrt(N)), between(1, UpperBound, D), 0 is N mod D, ( Divisor = D ; LargerDivisor is N/D, LargerDivisor =\= D, Divisor = LargerDivisor ). proper_divisor(N, D) :- divisor(N, D), D =\= N. assoc_num_divsSum_in_range(Low, High, Assoc) :- findall( Num-DivSum, ( between(Low, High, Num), aggregate_all( sum(D), proper_divisor(Num, D), DivSum )), Pairs ), list_to_assoc(Pairs, Assoc). get_amicable_pair(Assoc, M-N) :- gen_assoc(M, Assoc, N), M < N, get_assoc(N, Assoc, M). amicable_pairs_under_20000(Pairs) :- assoc_num_divsSum_in_range(1,20000, Assoc), findall(P, get_amicable_pair(Assoc, P), Pairs).  Output: ?- amicable_pairs_under_20000(R). R = [220-284, 1184-1210, 2620-2924, 5020-5564, 6232-6368, 10744-10856, 12285-14595, 17296-18416].  ## PureBasic EnableExplicit Procedure.i SumProperDivisors(Number) If Number < 2 : ProcedureReturn 0 : EndIf Protected i, sum = 0 For i = 1 To Number / 2 If Number % i = 0 sum + i EndIf Next ProcedureReturn sum EndProcedure Define n, f Define Dim sum(19999) If OpenConsole() For n = 1 To 19999 sum(n) = SumProperDivisors(n) Next PrintN("The pairs of amicable numbers below 20,000 are : ") PrintN("") For n = 1 To 19998 f = sum(n) If f <= n Or f < 1 Or f > 19999 : Continue : EndIf If f = sum(n) And n = sum(f) PrintN(RSet(Str(n),5) + " and " + RSet(Str(sum(n)), 5)) EndIf Next PrintN("") PrintN("Press any key to close the console") Repeat: Delay(10) : Until Inkey() <> "" CloseConsole() EndIf Output: The pairs of amicable numbers below 20,000 are : 220 and 284 1184 and 1210 2620 and 2924 5020 and 5564 6232 and 6368 10744 and 10856 12285 and 14595 17296 and 18416  ## Python Importing Proper divisors from prime factors: from proper_divisors import proper_divs def amicable(rangemax=20000): n2divsum = {n: sum(proper_divs(n)) for n in range(1, rangemax + 1)} for num, divsum in n2divsum.items(): if num < divsum and divsum <= rangemax and n2divsum[divsum] == num: yield num, divsum if __name__ == '__main__': for num, divsum in amicable(): print('Amicable pair: %i and %i With proper divisors:\n %r\n %r' % (num, divsum, sorted(proper_divs(num)), sorted(proper_divs(divsum))))  Output: Amicable pair: 220 and 284 With proper divisors: [1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110] [1, 2, 4, 71, 142] Amicable pair: 1184 and 1210 With proper divisors: [1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592] [1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605] Amicable pair: 2620 and 2924 With proper divisors: [1, 2, 4, 5, 10, 20, 131, 262, 524, 655, 1310] [1, 2, 4, 17, 34, 43, 68, 86, 172, 731, 1462] Amicable pair: 5020 and 5564 With proper divisors: [1, 2, 4, 5, 10, 20, 251, 502, 1004, 1255, 2510] [1, 2, 4, 13, 26, 52, 107, 214, 428, 1391, 2782] Amicable pair: 6232 and 6368 With proper divisors: [1, 2, 4, 8, 19, 38, 41, 76, 82, 152, 164, 328, 779, 1558, 3116] [1, 2, 4, 8, 16, 32, 199, 398, 796, 1592, 3184] Amicable pair: 10744 and 10856 With proper divisors: [1, 2, 4, 8, 17, 34, 68, 79, 136, 158, 316, 632, 1343, 2686, 5372] [1, 2, 4, 8, 23, 46, 59, 92, 118, 184, 236, 472, 1357, 2714, 5428] Amicable pair: 12285 and 14595 With proper divisors: [1, 3, 5, 7, 9, 13, 15, 21, 27, 35, 39, 45, 63, 65, 91, 105, 117, 135, 189, 195, 273, 315, 351, 455, 585, 819, 945, 1365, 1755, 2457, 4095] [1, 3, 5, 7, 15, 21, 35, 105, 139, 417, 695, 973, 2085, 2919, 4865] Amicable pair: 17296 and 18416 With proper divisors: [1, 2, 4, 8, 16, 23, 46, 47, 92, 94, 184, 188, 368, 376, 752, 1081, 2162, 4324, 8648] [1, 2, 4, 8, 16, 1151, 2302, 4604, 9208] Or, supplying our own properDivisors function, and defining the harvest in terms of a generic concatMap: '''Amicable pairs''' from itertools import chain from math import sqrt # amicablePairsUpTo :: Int -> [(Int, Int)] def amicablePairsUpTo(n): '''List of all amicable pairs of integers below n. ''' sigma = compose(sum)(properDivisors) def amicable(x): y = sigma(x) return [(x, y)] if (x < y and x == sigma(y)) else [] return concatMap(amicable)( enumFromTo(1)(n) ) # TEST ---------------------------------------------------- # main :: IO () def main(): '''Amicable pairs of integers up to 20000''' for x in amicablePairsUpTo(20000): print(x) # GENERIC ------------------------------------------------- # compose (<<<) :: (b -> c) -> (a -> b) -> a -> c def compose(g): '''Right to left function composition.''' return lambda f: lambda x: g(f(x)) # concatMap :: (a -> [b]) -> [a] -> [b] def concatMap(f): '''A concatenated list or string over which a function f has been mapped. The list monad can be derived by using an (a -> [b]) function which wraps its output in a list (using an empty list to represent computational failure). ''' return lambda xs: (''.join if isinstance(xs, str) else list)( chain.from_iterable(map(f, xs)) ) # enumFromTo :: Int -> Int -> [Int] def enumFromTo(m): '''Enumeration of integer values [m..n]''' def go(n): return list(range(m, 1 + n)) return lambda n: go(n) # properDivisors :: Int -> [Int] def properDivisors(n): '''Positive divisors of n, excluding n itself''' root_ = sqrt(n) intRoot = int(root_) blnSqr = root_ == intRoot lows = [x for x in range(1, 1 + intRoot) if 0 == n % x] return lows + [ n // x for x in reversed( lows[1:-1] if blnSqr else lows[1:] ) ] # MAIN --- if __name__ == '__main__': main()  Output: (220, 284) (1184, 1210) (2620, 2924) (5020, 5564) (6232, 6368) (10744, 10856) (12285, 14595) (17296, 18416) ## Quackery properdivisors is defined at Proper divisors#Quackery.  [ properdivisors dup size 0 = iff [ drop 0 ] done behead swap witheach + ] is spd ( n --> n ) [ dup dup spd dup spd rot = unrot > and ] is largeamicable ( n --> b ) [ [] swap times [ i^ largeamicable if [ i^ dup spd swap join nested join ] ] ] is amicables ( n --> [ ) 20000 amicables witheach [ witheach [ echo sp ] cr ] Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  ## R divisors <- function (n) { Filter( function (m) 0 == n %% m, 1:(n/2) ) } table = sapply(1:19999, function (n) sum(divisors(n)) ) for (n in 1:19999) { m = table[n] if ((m > n) && (m < 20000) && (n == table[m])) cat(n, " ", m, "\n") }  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  ## Racket With Proper_divisors#Racket in place: #lang racket (require "proper-divisors.rkt") (define SCOPE 20000) (define P (let ((P-v (vector))) (λ (n) (set! P-v (fold-divisors P-v n 0 +)) (vector-ref P-v n)))) ;; returns #f if not an amicable number, amicable pairing otherwise (define (amicable? n) (define m (P n)) (define m-sod (P m)) (and (= m-sod n) (< m n) ; each pair exactly once, also eliminates perfect numbers m)) (void (amicable? SCOPE)) ; prime the memoisation (for* ((n (in-range 1 (add1 SCOPE))) (m (in-value (amicable? n))) #:when m) (printf #<<EOS amicable pair: ~a, ~a ~a: divisors: ~a ~a: divisors: ~a EOS n m n (proper-divisors n) m (proper-divisors m)))  Output: amicable pair: 284, 220 284: divisors: (1 2 4 71 142) 220: divisors: (1 2 4 5 10 11 20 22 44 55 110) amicable pair: 1210, 1184 1210: divisors: (1 2 5 10 11 22 55 110 121 242 605) 1184: divisors: (1 2 4 8 16 32 37 74 148 296 592) amicable pair: 2924, 2620 2924: divisors: (1 2 4 17 34 43 68 86 172 731 1462) 2620: divisors: (1 2 4 5 10 20 131 262 524 655 1310) amicable pair: 5564, 5020 5564: divisors: (1 2 4 13 26 52 107 214 428 1391 2782) 5020: divisors: (1 2 4 5 10 20 251 502 1004 1255 2510) amicable pair: 6368, 6232 6368: divisors: (1 2 4 8 16 32 199 398 796 1592 3184) 6232: divisors: (1 2 4 8 19 38 41 76 82 152 164 328 779 1558 3116) amicable pair: 10856, 10744 10856: divisors: (1 2 4 8 23 46 59 92 118 184 236 472 1357 2714 5428) 10744: divisors: (1 2 4 8 17 34 68 79 136 158 316 632 1343 2686 5372) amicable pair: 14595, 12285 14595: divisors: (1 3 5 7 15 21 35 105 139 417 695 973 2085 2919 4865) 12285: divisors: (1 3 5 7 9 13 15 21 27 35 39 45 63 65 91 105 117 135 189 195 273 315 351 455 585 819 945 1365 1755 2457 4095) amicable pair: 18416, 17296 18416: divisors: (1 2 4 8 16 1151 2302 4604 9208) 17296: divisors: (1 2 4 8 16 23 46 47 92 94 184 188 368 376 752 1081 2162 4324 8648)  ## Raku (formerly Perl 6) Works with: Rakudo version 2019.03.1 sub propdivsum (\x) { my @l = 1 if x > 1; (2 .. x.sqrt.floor).map: -> \d { unless x % d { @l.push: d; my \y = x div d; @l.push: y if y != d } } sum @l } (1..20000).race.map: -> i { my j = propdivsum(i); say "i j" if j > i and i == propdivsum(j); }  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 ## REBOL ;- based on Lua code ;-) sum-of-divisors: func[n /local sum][ sum: 1 ; using to-integer for compatibility with Rebol2 for d 2 (to-integer square-root n) 1 [ if 0 = remainder n d [ sum: n / d + sum + d ] ] sum ] for n 2 20000 1 [ if n < m: sum-of-divisors n [ if n = sum-of-divisors m [ print [n tab m] ] ] ]  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  ## ReScript let isqrt = (v) => { Belt.Float.toInt( sqrt(Belt.Int.toFloat(v))) } let sum_divs = (n) => { let sum = ref(1) for d in 2 to isqrt(n) { if mod(n, d) == 0 { sum.contents = sum.contents + (n / d + d) } } sum.contents } { for n in 2 to 20000 { let m = sum_divs(n) if (m > n) { if sum_divs(m) == n { Printf.printf("%d %d\n", n, m) } } } } Output:  bsc ampairs.res > ampairs.bs.js  node ampairs.bs.js 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  ## REXX ### version 1, with factoring /*REXX*/ Call time 'R' Do x=1 To 20000 pd=proper_divisors(x) sumpd.x=sum(pd) End Say 'sum(pd) computed in' time('E') 'seconds' Call time 'R' Do x=1 To 20000 /* If x//1000=0 Then Say x time() */ Do y=x+1 To 20000 If y=sumpd.x &, x=sumpd.y Then Say x y 'found after' time('E') 'seconds' End End Say time('E') 'seconds total search time' Exit proper_divisors: Procedure Parse Arg n Pd='' If n=1 Then Return '' If n//2=1 Then /* odd number */ delta=2 Else /* even number */ delta=1 Do d=1 To n%2 By delta If n//d=0 Then pd=pd d End Return space(pd) sum: Procedure Parse Arg list sum=0 Do i=1 To words(list) sum=sum+word(list,i) End Return sum  Output: sum(pd) computed in 48.502000 seconds 220 284 found after 3.775000 seconds 1184 1210 found after 21.611000 seconds 2620 2924 found after 46.817000 seconds 5020 5564 found after 84.296000 seconds 6232 6368 found after 100.918000 seconds 10744 10856 found after 150.126000 seconds 12285 14595 found after 162.124000 seconds 17296 18416 found after 185.600000 seconds 188.836000 seconds total search time  ### version 2, using SIGMA function This REXX version allows the specification of the upper limit (for the searching of amicable pairs). Some optimization was incorporated by using a sigma function, which was a re-coded proper divisors (Pdivs) function, which was taken from the REXX language entry for Rosetta Code task integer factors. Other optimizations were incorporated which took advantage of several well-known generalizations about amicable pairs. The generation/summation is about 5,000% times faster than the 1st REXX version; searching is about 10,000% times faster. CPU time consumption note: for every doubling of H (the upper limit for searches), the CPU time consumed triples. /*REXX program calculates and displays all amicable pairs up to a given number. */ parse arg H .; if H=='' | H=="," then H= 20000 /*get optional arguments (high limit).*/ w= length(H) ; low= 220 /*W: used for columnar output alignment*/ @.=. /* [↑] LOW is lowest amicable number. */ do k=low for H-low; _= sigma(k) /*generate sigma sums for a range of #s*/ if _>=low then @.k= _ /*only keep the pertinent sigma sums. */ end /*k*/ /* [↑] process a range of integers. */ #= 0 /*number of amicable pairs found so far*/ do m=low to H; n= @.m /*start the search at the lowest number*/ if m==@.n then do /*If equal, might be an amicable number*/ if m==n then iterate /*Is this a perfect number? Then skip.*/ #= # + 1 /*bump the amicable pair counter. */ say right(m,w) ' and ' right(n,w) " are an amicable pair." m= n /*start M (DO index) from N. */ end end /*m*/ say say # ' amicable pairs found up to ' H /*display count of the amicable pairs. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ sigma: procedure; parse arg x; od= x // 2 /*use either EVEN or ODD integers. */ s= 1 /*set initial sigma sum to unity. ___*/ do j=2+od by 1+od while j*j<x /*divide by all integers up to the √ X */ if x//j==0 then s= s + j + x%j /*add the two divisors to the sum. */ end /*j*/ /* [↑] % is REXX integer division. */ /* ___ */ if j*j==x then return s + j /*Was X a square? If so, add √ X */ return s /*return (sigma) sum of the divisors. */  output when using the default input:  220 and 284 are an amicable pair. 1184 and 1210 are an amicable pair. 2620 and 2924 are an amicable pair. 5020 and 5564 are an amicable pair. 6232 and 6368 are an amicable pair. 10744 and 10856 are an amicable pair. 12285 and 14595 are an amicable pair. 17296 and 18416 are an amicable pair. 8 amicable pairs found up to 20000  ### version 3, SIGMA with limited searches This REXX version is optimized to take advantage of the lowest ending-single-digit amicable number, and also incorporates the search of amicable numbers into the generation of the sigmas of the integers. The optimization makes it about another 30% faster when searching for amicable numbers up to one million. /*REXX program calculates and displays all amicable pairs up to a given number. */ parse arg H .; if H=='' | H=="," then H=20000 /*get optional arguments (high limit).*/ w=length(H) ; low=220 /*W: used for columnar output alignment*/ x= 220 34765731 6232 87633 284 12285 10856 36939357 6368 5684679 /*S minimums.*/ do i=0 for 10; .i= word(x, i + 1); end /*minimum amicable #s for last dec dig.*/ @.= /* [↑] LOW is lowest amicable number. */ #= 0 /*number of amicable pairs found so far*/ do k=low for H-low /*generate sigma sums for a range of #s*/ parse var k '' -1 D /*obtain last decimal digit of K. */ if k<.D then iterate /*if no need to compute, then skip it. */ _= sigma(k) /*generate sigma sum for the number K.*/ @.k= _ /*only keep the pertinent sigma sums. */ if k==@._ then do /*is it a possible amicable number ? */ if _==k then iterate /*Is it a perfect number? Then skip it*/ #= # + 1 /*bump the amicable pair counter. */ say right(_, w) ' and ' right(k, w) " are an amicable pair." end end /*k*/ /* [↑] process a range of integers. */ say say # 'amicable pairs found up to' H /*display the count of amicable pairs. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ sigma: procedure; parse arg x; od= x // 2 /*use either EVEN or ODD integers. */ s= 1 /*set initial sigma sum to unity. ___*/ do j=2+od by 1+od while j*j<x /*divide by all integers up to the √ x */ if x//j==0 then s= s + j + x%j /*add the two divisors to the sum. */ end /*j*/ /* [↑] % is REXX integer division. */ /* ___ */ if j*j==x then return s + j /*Was X a square? If so, add √ X */ return s /*return (sigma) sum of the divisors. */  output is identical to the 2nd REXX version. ### version 4, SIGMA using integer SQRT This REXX version is optimized to use the integer square root of X in the sigma function (instead of computing the square of J to see if that value exceeds X). The optimization makes it about another 20% faster when searching for amicable numbers up to one million. /*REXX program calculates and displays all amicable pairs up to a given number. */ parse arg H .; if H=='' | H=="," then H=20000 /*get optional arguments (high limit).*/ w= length(H) ; low= 220 /*W: used for columnar output alignment*/ x= 220 34765731 6232 87633 284 12285 10856 36939357 6368 5684679 /*S minimums.*/ do i=0 for 10; .i= word(x, i + 1); end /*minimum amicable #s for last dec dig.*/ @.= /* [↑] LOW is lowest amicable number. */ #= 0 /*number of amicable pairs found so far*/ do k=low for H-low /*generate sigma sums for a range of #s*/ parse var k '' -1 D /*obtain last decimal digit of K. */ if k<.D then iterate /*if no need to compute, then skip it. */ _= sigma(k) /*generate sigma sum for the number K.*/ @.k= _ /*only keep the pertinent sigma sums. */ if k==@._ then do /*is it a possible amicable number ? */ if _==k then iterate /*Is it a perfect number? Then skip it*/ #= # + 1 /*bump the amicable pair counter. */ say right(_, w) ' and ' right(k, w) " are an amicable pair." end end /*k*/ /* [↑] process a range of integers. */ say say # 'amicable pairs found up to' H /*display the count of amicable pairs. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ iSqrt: procedure; parse arg x; r= 0; q= 1; do while q<=x; q= q * 4; end do while q>1; q=q%4; _=x-r-q; r=r%2; if _>=0 then do;x=_;r=r+q; end; end return r /*──────────────────────────────────────────────────────────────────────────────────────*/ sigma: procedure; parse arg x; od= x // 2 /*use either EVEN or ODD integers. */ s= 1 /*set initial sigma sum to unity. ___*/ do j=2+od by 1+od to iSqrt(x) /*divide by all integers up to the √ x */ if x//j==0 then s= s + j + x%j /*add the two divisors to the sum. */ end /*j*/ /* [↑] % is the REXX integer division.*/ /* ___ */ if j*j==x then return s + j /*Was X a square? If so, add √ X */ return s /*return (sigma) sum of the divisors. */  output is identical to the 2nd REXX version. ### version 5, SIGMA (in-line code) This REXX version is optimized by bringing the functions in-line (which minimizes the overhead of invoking two internal functions), and it also pre-computes the powers of four (for the integer square root code). This method of coding has the disadvantage in that the code (logic) is less idiomatic and therefore less readable. The optimization makes it about another 15% faster when searching for amicable numbers up to one million. /*REXX program calculates and displays all amicable pairs up to a given number. */ parse arg H .; if H=='' | H=="," then H=20000 /*get optional arguments (high limit).*/ w= length(H) ; low= 220 /*W: used for columnar output alignment*/ x= 220 34765731 6232 87633 284 12285 10856 36939357 6368 5684679 /*S minimums.*/ do i=0 for 10; .i= word(x, i + 1); end /*minimum amicable #s for last dec dig.*/ @.= /* [↑] LOW is lowest amicable number. */ #= 0 /*number of amicable pairs found so far*/ do k=low for H-low /*generate sigma sums for a range of #s*/ parse var k '' -1 D /*obtain last decimal digit of K. */ if k<.D then iterate /*if no need to compute, then skip it. */ _= sigma(k) /*generate sigma sum for the number K.*/ @.k= _ /*only keep the pertinent sigma sums. */ if k==@._ then do /*is it a possible amicable number ? */ if _==k then iterate /*Is it a perfect number? Then skip it*/ #= # + 1 /*bump the amicable pair counter. */ say right(_, w) ' and ' right(k, w) " are an amicable pair." end end /*k*/ /* [↑] process a range of integers. */ say say # 'amicable pairs found up to' H /*display the count of amicable pairs. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ iSqrt: procedure; parse arg x; r= 0; q= 1; do while q<=x; q= q * 4; end do while q>1; q=q%4; _=x-r-q; r=r%2; if _>=0 then do;x=_;r=r+q; end; end return r /*──────────────────────────────────────────────────────────────────────────────────────*/ sigma: procedure; parse arg x; od= x // 2 /*use either EVEN or ODD integers. */ s= 1 /*set initial sigma sum to unity. ___*/ do j=2+od by 1+od to iSqrt(x) /*divide by all integers up to the √ x */ if x//j==0 then s= s + j + x%j /*add the two divisors to the sum. */ end /*j*/ /* [↑] % is the REXX integer division.*/ /* ___ */ if j*j==x then return s + j /*Was X a square? If so, add √ X */ return s /*return (sigma) sum of the divisors. */  output is identical to the 2nd REXX version. ## Ring size = 18500 for n = 1 to size m = amicable(n) if m>n and amicable(m)=n see "" + n + " and " + m + nl ok next see "OK" + nl func amicable nr sum = 1 for d = 2 to sqrt(nr) if nr % d = 0 sum = sum + d sum = sum + nr / d ok next return sum ## RPL Works with: HP version 49 ≪ {} 2 ROT FOR j IF DUP j POS NOT THEN @ avoiding duplicates j DIVIS ∑LIST j - DUP IF DUP 1 ≠ OVER j ≠ AND THEN IF DUP DIVIS ∑LIST SWAP - j == THEN + j + ELSE DROP END ELSE DROP2 END END NEXT {} 1 3 PICK SIZE FOR j @ formatting the list for output OVER j DUP 1 + SUB REVLIST 1 →LIST + 2 STEP NIP ≫ 'TASK' STO  200000 TASK  Output: 1: {{220 284} {1184 1210} {2620 2924} {5020 5564} {6232 6368} {10744 10856} {12285 14595} {17296 18416}}  ## Ruby With proper_divisors#Ruby in place: h = {} (1..20_000).each{|n| h[n] = n.proper_divisors.sum } h.select{|k,v| h[v] == k && k < v}.each do |key,val| # k<v filters out doubles and perfects puts "#{key} and #{val}" end  Output:  220 and 284 1184 and 1210 2620 and 2924 5020 and 5564 6232 and 6368 10744 and 10856 12285 and 14595 17296 and 18416  ## Run BASIC size = 18500 for n = 1 to size m = amicable(n) if m > n and amicable(m) = n then print n ; " and " ; m next function amicable(nr) amicable = 1 for d = 2 to sqr(nr) if nr mod d = 0 then amicable = amicable + d + nr / d next end function 220 and 284 1184 and 1210 2620 and 2924 5020 and 5564 6232 and 6368 10744 and 10856 12285 and 14595 17296 and 18416  ## Rust fn sum_of_divisors(val: u32) -> u32 { (1..val/2+1).filter(|n| val % n == 0) .fold(0, |sum, n| sum + n) } fn main() { let iter = (1..20_000).map(|i| (i, sum_of_divisors(i))) .filter(|&(i, div_sum)| i > div_sum); for (i, sum1) in iter { if sum_of_divisors(sum1) == i { println!("{} {}", i, sum1); } } }  Output: 284 220 1210 1184 2924 2620 5564 5020 6368 6232 10856 10744 14595 12285 18416 17296  Translation of: Python fn main() { const RANGE_MAX: u32 = 20_000; let proper_divs = |n: u32| -> Vec<u32> { (1..=(n + 1) / 2).filter(|&x| n % x == 0).collect() }; let n2d: Vec<u32> = (1..=RANGE_MAX).map(|n| proper_divs(n).iter().sum()).collect(); for (n, &div_sum) in n2d.iter().enumerate() { let n = n as u32 + 1; if n < div_sum && div_sum <= RANGE_MAX && n2d[div_sum as usize - 1] == n { println!("Amicable pair: {} and {} with proper divisors:", n, div_sum); println!(" {:?}", proper_divs(n)); println!(" {:?}", proper_divs(div_sum)); } } }  Output: Amicable pair: 220 and 284 with proper divisors: [1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110] [1, 2, 4, 71, 142] Amicable pair: 1184 and 1210 with proper divisors: [1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592] [1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605] Amicable pair: 2620 and 2924 with proper divisors: [1, 2, 4, 5, 10, 20, 131, 262, 524, 655, 1310] [1, 2, 4, 17, 34, 43, 68, 86, 172, 731, 1462] Amicable pair: 5020 and 5564 with proper divisors: [1, 2, 4, 5, 10, 20, 251, 502, 1004, 1255, 2510] [1, 2, 4, 13, 26, 52, 107, 214, 428, 1391, 2782] Amicable pair: 6232 and 6368 with proper divisors: [1, 2, 4, 8, 19, 38, 41, 76, 82, 152, 164, 328, 779, 1558, 3116] [1, 2, 4, 8, 16, 32, 199, 398, 796, 1592, 3184] Amicable pair: 10744 and 10856 with proper divisors: [1, 2, 4, 8, 17, 34, 68, 79, 136, 158, 316, 632, 1343, 2686, 5372] [1, 2, 4, 8, 23, 46, 59, 92, 118, 184, 236, 472, 1357, 2714, 5428] Amicable pair: 12285 and 14595 with proper divisors: [1, 3, 5, 7, 9, 13, 15, 21, 27, 35, 39, 45, 63, 65, 91, 105, 117, 135, 189, 195, 273, 315, 351, 455, 585, 819, 945, 1365, 1755, 2457, 4095] [1, 3, 5, 7, 15, 21, 35, 105, 139, 417, 695, 973, 2085, 2919, 4865] Amicable pair: 17296 and 18416 with proper divisors: [1, 2, 4, 8, 16, 23, 46, 47, 92, 94, 184, 188, 368, 376, 752, 1081, 2162, 4324, 8648] [1, 2, 4, 8, 16, 1151, 2302, 4604, 9208]  ## Sage # Define the sum of proper divisors function def sum_of_proper_divisors(n): return sum(divisors(n)) - n # Iterate over the desired range for x in range(1, 20001): y = sum_of_proper_divisors(x) if y > x: if x == sum_of_proper_divisors(y): print(f"{x} {y}")  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  ## S-BASIC lines constant search_limit = 20000 var a, b, count = integer dim integer sumf(search_limit) print "Searching up to"; search_limit; " for amicable pairs:" rem - set up the table of proper divisor sums for a = 1 to search_limit sumf(a) = 1 next a for a = 2 to search_limit b = a + a while (b > 0) and (b <= search_limit) do begin sumf(b) = sumf(b) + a b = b + a end next a rem - search for pairs using the table count = 0 for a = 2 to search_limit b = sumf(a) if (b > a) and (b < search_limit) then if a = sumf(b) then begin print using "##### #####"; a; b count = count + 1 end next a print count; " pairs were found" end  Output: Searching up to 20000 for amicable pairs: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 8 pairs were found  ## Scala def properDivisors(n: Int) = (1 to n/2).filter(i => n % i == 0) val divisorsSum = (1 to 20000).map(i => i -> properDivisors(i).sum).toMap val result = divisorsSum.filter(v => v._1 < v._2 && divisorsSum.get(v._2) == Some(v._1)) println( result mkString ", " )  Output: 5020 -> 5564, 220 -> 284, 6232 -> 6368, 17296 -> 18416, 2620 -> 2924, 10744 -> 10856, 12285 -> 14595, 1184 -> 1210 ## Scheme (import (scheme base) (scheme inexact) (scheme write) (only (srfi 1) fold)) ;; return a list of the proper-divisors of n (define (proper-divisors n) (let ((root (sqrt n))) (let loop ((divisors (list 1)) (i 2)) (if (> i root) divisors (loop (if (zero? (modulo n i)) (if (= (square i) n) (cons i divisors) (append (list i (quotient n i)) divisors)) divisors) (+ 1 i)))))) (define (sum-proper-divisors n) (if (< n 2) 0 (fold + 0 (proper-divisors n)))) (define *max-n* 20000) ;; hold sums of proper divisors in a cache, to avoid recalculating (define *cache* (make-vector (+ 1 *max-n*))) (for-each (lambda (i) (vector-set! *cache* i (sum-proper-divisors i))) (iota *max-n* 1)) (define (amicable-pair? i j) (and (not (= i j)) (= i (vector-ref *cache* j)) (= j (vector-ref *cache* i)))) ;; double loop to *max-n*, displaying all amicable pairs (let loop-i ((i 1)) (when (<= i *max-n*) (let loop-j ((j i)) (when (<= j *max-n*) (when (amicable-pair? i j) (display (string-append "Amicable pair: " (number->string i) " " (number->string j))) (newline)) (loop-j (+ 1 j)))) (loop-i (+ 1 i))))  Output: Amicable pair: 220 284 Amicable pair: 1184 1210 Amicable pair: 2620 2924 Amicable pair: 5020 5564 Amicable pair: 6232 6368 Amicable pair: 10744 10856 Amicable pair: 12285 14595 Amicable pair: 17296 18416  ## SETL program amicable_pairs; p := propDivSums(20000); loop for [n,m] in p | n = p(p(n)) and n<m do print([n,m]); end loop; proc propDivSums(n); divs := {}; loop for i in [1..n] do loop for j in [i*2, i*3..n] do divs(j) +:= i; end loop; end loop; return divs; end proc; end program; Output: [220 284] [1184 1210] [2620 2924] [5020 5564] [6232 6368] [10744 10856] [12285 14595] [17296 18416] ## Sidef func propdivsum(n) { n.sigma - n } for i in (1..20000) { var j = propdivsum(i) say "#{i} #{j}" if (j>i && i==propdivsum(j)) }  Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416  ## Swift import func Darwin.sqrt func sqrt(x:Int) -> Int { return Int(sqrt(Double(x))) } func properDivs(n: Int) -> [Int] { if n == 1 { return [] } var result = [Int]() for div in filter (1...sqrt(n), { n % 0 == 0 }) { result.append(div) if n/div != div && n/div != n { result.append(n/div) } } return sorted(result) } func sumDivs(n:Int) -> Int { struct Cache { static var sum = [Int:Int]() } if let sum = Cache.sum[n] { return sum } let sum = properDivs(n).reduce(0) { 0 + 1 } Cache.sum[n] = sum return sum } func amicable(n:Int, m:Int) -> Bool { if n == m { return false } if sumDivs(n) != m || sumDivs(m) != n { return false } return true } var pairs = [(Int, Int)]() for n in 1 ..< 20_000 { for m in n+1 ... 20_000 { if amicable(n, m) { pairs.append(n, m) println("\(n, m)") } } }  ### Alternative about 800 times faster. import func Darwin.sqrt func sqrt(x:Int) -> Int { return Int(sqrt(Double(x))) } func sigma(n: Int) -> Int { if n == 1 { return 0 } // definition of aliquot sum var result = 1 let root = sqrt(n) for var div = 2; div <= root; ++div { if n % div == 0 { result += div + n/div } } if root*root == n { result -= root } return (result) } func amicables (upTo: Int) -> () { var aliquot = Array(count: upTo+1, repeatedValue: 0) for i in 1 ... upTo { // fill lookup array aliquot[i] = sigma(i) } for i in 1 ... upTo { let a = aliquot[i] if a > upTo {continue} //second part of pair out-of-bounds if a == i {continue} //skip perfect numbers if i == aliquot[a] { print("\(i, a)") aliquot[a] = upTo+1 //prevent second display of pair } } } amicables(20_000)  Output: (220, 284) (1184, 1210) (2620, 2924) (5020, 5564) (6232, 6368) (10744, 10856) (12285, 14595) (17296, 18416)  ## tbas dim sums(20000) sub sum_proper_divisors(n) dim sum = 0 dim i if n > 1 then for i = 1 to (n \ 2) if n %% i = 0 then sum = sum + i end if next end if return sum end sub dim i, j for i = 1 to 20000 sums(i) = sum_proper_divisors(i) for j = i-1 to 2 by -1 if sums(i) = j and sums(j) = i then print "Amicable pair:";sums(i);"-";sums(j) exit for end if next next >tbas amicable_pairs.bas Amicable pair: 220 - 284 Amicable pair: 1184 - 1210 Amicable pair: 2620 - 2924 Amicable pair: 5020 - 5564 Amicable pair: 6232 - 6368 Amicable pair: 10744 - 10856 Amicable pair: 12285 - 14595 Amicable pair: 17296 - 18416  ## Tcl proc properDivisors {n} { if {n == 1} return set divs 1 set sum 1 for {set i 2} {i*i <= n} {incr i} { if {!(n % i)} { lappend divs i incr sum i if {i*i < n} { lappend divs [set d [expr {n / i}]] incr sum d } } } return [list sum divs] } proc amicablePairs {limit} { set result {} set sums [set divs {{}}] for {set n 1} {n < limit} {incr n} { lassign [properDivisors n] sum d lappend sums sum lappend divs [lsort -integer d] } for {set n 1} {n < limit} {incr n} { set nsum [lindex sums n] for {set m 1} {m < n} {incr m} { if {n==[lindex sums m] && m==nsum} { lappend result m n [lindex divs m] [lindex divs n] } } } return result } foreach {m n md nd} [amicablePairs 20000] { puts "m and n are an amicable pair with these proper divisors" puts "\tm : md" puts "\tn : nd" }  Output: 220 and 284 are an amicable pair with these proper divisors 220 : 1 2 4 5 10 11 20 22 44 55 110 284 : 1 2 4 71 142 1184 and 1210 are an amicable pair with these proper divisors 1184 : 1 2 4 8 16 32 37 74 148 296 592 1210 : 1 2 5 10 11 22 55 110 121 242 605 2620 and 2924 are an amicable pair with these proper divisors 2620 : 1 2 4 5 10 20 131 262 524 655 1310 2924 : 1 2 4 17 34 43 68 86 172 731 1462 5020 and 5564 are an amicable pair with these proper divisors 5020 : 1 2 4 5 10 20 251 502 1004 1255 2510 5564 : 1 2 4 13 26 52 107 214 428 1391 2782 6232 and 6368 are an amicable pair with these proper divisors 6232 : 1 2 4 8 19 38 41 76 82 152 164 328 779 1558 3116 6368 : 1 2 4 8 16 32 199 398 796 1592 3184 10744 and 10856 are an amicable pair with these proper divisors 10744 : 1 2 4 8 17 34 68 79 136 158 316 632 1343 2686 5372 10856 : 1 2 4 8 23 46 59 92 118 184 236 472 1357 2714 5428 12285 and 14595 are an amicable pair with these proper divisors 12285 : 1 3 5 7 9 13 15 21 27 35 39 45 63 65 91 105 117 135 189 195 273 315 351 455 585 819 945 1365 1755 2457 4095 14595 : 1 3 5 7 15 21 35 105 139 417 695 973 2085 2919 4865 17296 and 18416 are an amicable pair with these proper divisors 17296 : 1 2 4 8 16 23 46 47 92 94 184 188 368 376 752 1081 2162 4324 8648 18416 : 1 2 4 8 16 1151 2302 4604 9208  ## Transd #lang transd MainModule : { _start: (lambda (with sum 0 d 0 f Filter( from: 1 to: 20000 apply: (lambda (= sum 1) (for i in Range(2 (to-Int (sqrt @it))) do (if (not (mod @it i)) (= d (/ @it i)) (+= sum i) (if (neq d i) (+= sum d)))) (ret sum))) (with v (to-vector f) (for i in v do (if (and (< i (size v)) (eq (+ @idx 1) (get v (- i 1))) (< i (get v (- i 1)))) (textout (+ @idx 1) ", " i "\n") ))))) }  Output: 284, 220 1210, 1184 2924, 2620 5564, 5020 6368, 6232 10856, 10744 14595, 12285 18416, 17296  ## uBasic/4tH Input "Limit: ";l Print "Amicable pairs < ";l For n = 1 To l m = FUNC(_SumDivisors (n))-n If m = 0 Then Continue ' No division by zero, please p = FUNC(_SumDivisors (m))-m If (n=p) * (n<m) Then Print n;" and ";m Next End _LeastPower Param(2) Local(1) c@ = a@ Do While (b@ % c@) = 0 c@ = c@ * a@ Loop Return (c@) ' Return the sum of the proper divisors of a@ _SumDivisors Param(1) Local(4) b@ = a@ c@ = 1 ' Handle two specially d@ = FUNC(_LeastPower (2,b@)) c@ = c@ * (d@ - 1) b@ = b@ / (d@ / 2) ' Handle odd factors For e@ = 3 Step 2 While (e@*e@) < (b@+1) d@ = FUNC(_LeastPower (e@,b@)) c@ = c@ * ((d@ - 1) / (e@ - 1)) b@ = b@ / (d@ / e@) Loop ' At this point, t must be one or prime If (b@ > 1) c@ = c@ * (b@+1) Return (c@)  Output: Limit: 20000 Amicable pairs < 20000 220 and 284 1184 and 1210 2620 and 2924 5020 and 5564 6232 and 6368 10744 and 10856 12285 and 14595 17296 and 18416 0 OK, 0:238 ## UTFool ··· http://rosettacode.org/wiki/Amicable_pairs ··· ■ AmicablePairs § static ▶ main • args⦂ String[] ∀ n ∈ 1…20000 m⦂ int: sumPropDivs n if m < n = sumPropDivs m System.out.println "⸨m⸩ ; ⸨n⸩" ▶ sumPropDivs⦂ int • n⦂ int m⦂ int: 1 ∀ i ∈ √n ⋯> 1 m +: n \ i = 0 ? i + (i = n / i ? 0 ! n / i) ! 0 ⏎ m ## VBA Option Explicit Public Sub AmicablePairs() Dim a(2 To 20000) As Long, c As New Collection, i As Long, j As Long, t# t = Timer For i = LBound(a) To UBound(a) 'collect the sum of the proper divisors 'of each numbers between 2 and 20000 a(i) = S(i) Next 'Double Loops to test the amicable For i = LBound(a) To UBound(a) For j = i + 1 To UBound(a) If i = a(j) Then If a(i) = j Then On Error Resume Next c.Add i & " : " & j, CStr(i * j) On Error GoTo 0 Exit For End If End If Next Next 'End. Return : Debug.Print "Execution Time : " & Timer - t & " seconds." Debug.Print "Amicable pairs below 20 000 are : " For i = 1 To c.Count Debug.Print c.Item(i) Next i End Sub Private Function S(n As Long) As Long 'returns the sum of the proper divisors of n Dim j As Long For j = 1 To n \ 2 If n Mod j = 0 Then S = j + S Next End Function Output: Execution Time : 7,95703125 seconds. Amicable pairs below 20 000 are : 220 : 284 1184 : 1210 2620 : 2924 5020 : 5564 6232 : 6368 10744 : 10856 12285 : 14595 17296 : 18416 ## VBScript Not at all optimal. :-( start = Now Set nlookup = CreateObject("Scripting.Dictionary") Set uniquepair = CreateObject("Scripting.Dictionary") For i = 1 To 20000 sum = 0 For n = 1 To 20000 If n < i Then If i Mod n = 0 Then sum = sum + n End If End If Next nlookup.Add i,sum Next For j = 1 To 20000 sum = 0 For m = 1 To 20000 If m < j Then If j Mod m = 0 Then sum = sum + m End If End If Next If nlookup.Exists(sum) And nlookup.Item(sum) = j And j <> sum _ And uniquepair.Exists(sum) = False Then uniquepair.Add j,sum End If Next For Each key In uniquepair.Keys WScript.Echo key & ":" & uniquepair.Item(key) Next WScript.Echo "Execution Time: " & DateDiff("s",Start,Now) & " seconds"  Output: 220:284 1184:1210 2620:2924 5020:5564 6232:6368 10744:10856 12285:14595 17296:18416 Execution Time: 162 seconds ## V (Vlang) Translation of: Go fn pfac_sum(i int) int { mut sum := 0 for p := 1; p <= i / 2; p++{ if i % p == 0 { sum += p } } return sum } fn main(){ a := []int{len: 20000, init:pfac_sum(it)} println('The amicable pairs below 20,000 are:') for n in 2 .. a.len { m := a[n] if m > n && m < 20000 && n == a[m] { println('{n:5} and {m:5}') } } }  Output: The amicable pairs below 20,000 are: 220 and 284 1184 and 1210 2620 and 2924 5020 and 5564 6232 and 6368 10744 and 10856 12285 and 14595 17296 and 18416  ## VTL-2 10 M=20000 20 I=1 30 :I)=1 40 I=I+1 50 #=M>I*30 60 I=2 70 J=I+I 80 :J)=:J)+I 90 J=J+I 100 #=M>J*80 110 I=I+1 120 #=(M/2)>I*70 130 I=1 140 J=:I) 150 #=(I<J)*I=:J)*190 160 I=I+1 170 #=M>I*140 180 #=999 190 ?=I 200 =9 210 ?=J 220 ?="" 230 #=! Output: 220 284 1184 1210 2620 2924 5020 5564 6232 6368 10744 10856 12285 14595 17296 18416 ## Wren Library: Wren-fmt Library: Wren-math import "./fmt" for Fmt import "./math" for Int, Nums var a = List.filled(20000, 0) for (i in 1...20000) a[i] = Nums.sum(Int.properDivisors(i)) System.print("The amicable pairs below 20,000 are:") for (n in 2...19999) { var m = a[n] if (m > n && m < 20000 && n == a[m]) { Fmt.print(" 5d and 5d", n, m) } }  Output: The amicable pairs below 20,000 are: 220 and 284 1184 and 1210 2620 and 2924 5020 and 5564 6232 and 6368 10744 and 10856 12285 and 14595 17296 and 18416  ## XPL0 func SumDiv(Num); \Return sum of proper divisors of Num int Num, Div, Sum, Quot; [Div:= 2; Sum:= 0; loop [Quot:= Num/Div; if Div > Quot then quit; if rem(0) = 0 then [Sum:= Sum + Div; if Div # Quot then Sum:= Sum + Quot; ]; Div:= Div+1; ]; return Sum+1; ]; def Limit = 20000; int Tbl(Limit), N, M; [for N:= 0 to Limit-1 do Tbl(N):= SumDiv(N); for N:= 1 to Limit-1 do [M:= Tbl(N); if M<Limit & N=Tbl(M) & M>N then [IntOut(0, N); ChOut(0, 9\tab;
IntOut(0, M);  CrLf(0);
];
];
]
Output:
220     284
1184    1210
2620    2924
5020    5564
6232    6368
10744   10856
12285   14595
17296   18416


## Yabasic

Translation of: Lua
sub sumDivs(n)
local sum, d

sum = 1

for d = 2 to sqrt(n)
if not mod(n, d) then
sum = sum + d
sum = sum + n / d
end if
next
return sum
end sub

for n = 2 to 20000
m = sumDivs(n)
if m > n then
if sumDivs(m) = n print n, "\t", m
end if
next

print : print peek("millisrunning"), " ms"

## Zig

const MAXIMUM: u32 = 20_000;

// Fill up a given array with arr[n] = sum(propDivs(n))
pub fn calcPropDivs(divs: []u32) void {
for (divs) |*d| d.* = 1;
var i: u32 = 2;
while (i <= divs.len/2) : (i += 1) {
var j = i * 2;
while (j < divs.len) : (j += i)
divs[j] += i;
}
}

// Are (A, B) an amicable pair?
pub fn amicable(divs: []const u32, a: u32, b: u32) bool {
return divs[a] == b and a == divs[b];
}

pub fn main() !void {
const stdout = @import("std").io.getStdOut().writer();

var divs: [MAXIMUM + 1]u32 = undefined;
calcPropDivs(divs[0..]);

var a: u32 = 1;
while (a < divs.len) : (a += 1) {
var b = a+1;
while (b < divs.len) : (b += 1) {
if (amicable(divs[0..], a, b))
try stdout.print("{d}, {d}\n", .{a, b});
}
}
}

Output:
220, 284
1184, 1210
2620, 2924
5020, 5564
6232, 6368
10744, 10856
12285, 14595
17296, 18416

## zkl

Slooooow

fcn properDivs(n){ [1.. (n + 1)/2 + 1].filter('wrap(x){ n%x==0 and n!=x }) }
const N=20000;
sums:=[1..N].pump(T(-1),fcn(n){ properDivs(n).sum(0) });
[0..].zip(sums).filter('wrap([(n,s)]){ (n<s<=N) and sums[s]==n }).println();
Output:
L(L(220,284),L(1184,1210),L(2620,2924),L(5020,5564),L(6232,6368),L(10744,10856),L(12285,14595),L(17296,18416))


## ZX Spectrum Basic

Translation of: AWK
10 LET limit=20000
20 PRINT "Amicable pairs < ";limit
30 FOR n=1 TO limit
40 LET num=n: GO SUB 1000
50 LET m=num
60 GO SUB 1000
70 IF n=num AND n<m THEN PRINT n;" ";m
80 NEXT n
90 STOP
1000 REM sumprop
1010 IF num<2 THEN LET num=0: RETURN
1020 LET sum=1
1030 LET root=SQR num
1040 FOR i=2 TO root-.01
1050 IF num/i=INT (num/i) THEN LET sum=sum+i+num/i
1060 NEXT i
1070 IF num/root=INT (num/root) THEN LET sum=sum+root
1080 LET num=sum
1090 RETURN
Output:
Amicable pairs < 20000
220 284
1184 1210
2620 2924
5020 5564
6232 6368
10744 10856
12285 14595
17296 18416`