Sum of divisors
Sum of divisors is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Given a positive integer, sum its positive divisors.
- Task
Show the result for the first 100 positive integers.
11l
F sum_of_divisors(n)
V ans = 0
V i = 1
V j = 1
L i * i <= n
I 0 == n % i
ans += i
j = n I/ i
I j != i
ans += j
i++
R ans
print((1..100).map(n -> sum_of_divisors(n)))- Output:
[1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84, 144, 68, 126, 96, 144, 72, 195, 74, 114, 124, 140, 96, 168, 80, 186, 121, 126, 84, 224, 108, 132, 120, 180, 90, 234, 112, 168, 128, 144, 120, 252, 98, 171, 156, 217]
Action!
PROC PrintNum(BYTE x)
Put(32)
IF x<10 THEN Put(32) FI
IF x<100 THEN Put(32) FI
PrintB(x)
RETURN
PROC Main()
DEFINE MAX="100"
BYTE ARRAY div(MAX+1)
BYTE i,j,LMARGIN=$52,oldLMARGIN
oldLMARGIN=LMARGIN
LMARGIN=0 ;remove left margin on the screen
Put(125) PutE() ;clear the screen
SetBlock(div,MAX+1,1)
FOR i=2 TO MAX
DO
FOR j=i TO MAX STEP i
DO
div(j)==+i
OD
OD
FOR i=1 TO MAX
DO
PrintNum(div(i))
OD
LMARGIN=oldLMARGIN ;restore left margin on the screen
RETURN- Output:
Screenshot from Atari 8-bit computer
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
ALGOL 68
...via Algol WBEGIN # sum the divisors of the first 100 positive integers #
# computes the sum of the divisors of v using the prime factorisation #
PROC divisor sum = ( INT v )INT:
BEGIN
INT total := 1, power := 2, n := v;
WHILE NOT ODD n DO # Deal with powers of 2 first #
total +:= power;
power *:= 2;
n OVERAB 2
OD;
INT p := 3; # Odd prime factors up to the square root #
WHILE ( p * p ) <= n DO
INT sum := 1;
power := p;
WHILE n MOD p = 0 DO
sum +:= power;
power *:= p;
n OVERAB p
OD;
p +:= 2;
total *:= sum
OD;
IF n > 1 THEN total *:= n + 1 FI; # If n > 1 then it's prime #
total
END # divisor sum # ;
BEGIN # show the first 100 divisor sums #
INT limit = 100;
print( ( "Sum of divisors for the first ", whole( limit, 0 ), " positive integers:" ) );
FOR n TO limit DO
IF n MOD 10 = 1 THEN print( ( newline ) ) FI;
print( ( " ", whole( divisor sum( n ), -4 ) ) )
OD
END
END- Output:
Sum of divisors for the first 100 positive integers:
1 3 4 7 6 12 8 15 13 18
12 28 14 24 24 31 18 39 20 42
32 36 24 60 31 42 40 56 30 72
32 63 48 54 48 91 38 60 56 90
42 96 44 84 78 72 48 124 57 93
72 98 54 120 72 120 80 90 60 168
62 96 104 127 84 144 68 126 96 144
72 195 74 114 124 140 96 168 80 186
121 126 84 224 108 132 120 180 90 234
112 168 128 144 120 252 98 171 156 217
ALGOL-M
begin
integer N;
N := 100;
begin
integer array div[1:N];
integer i, j, col;
for i := 1 step 1 until N do div[i] := 1;
for i := 2 step 1 until N do
for j := i step i until N do
div[j] := div[j] + i;
col := 0;
for i := 1 step 1 until N do begin
if (col-1)/10 <> col/10 then
write(div[i])
else
writeon(div[i]);
col := col + 1;
end;
end;
end- Output:
1 3 4 7 6 12 8 15 13 18
12 28 14 24 24 31 18 39 20 42
32 36 24 60 31 42 40 56 30 72
32 63 48 54 48 91 38 60 56 90
42 96 44 84 78 72 48 124 57 93
72 98 54 120 72 120 80 90 60 168
62 96 104 127 84 144 68 126 96 144
72 195 74 114 124 140 96 168 80 186
121 126 84 224 108 132 120 180 90 234
112 168 128 144 120 252 98 171 156 217
ALGOL W
begin % sum the divisors of the first 100 positive integers %
% computes the sum of the divisors of n using the prime %
% factorisation %
integer procedure divisor_sum( integer value v ) ; begin
integer total, power, n, p;
total := 1; power := 2; n := v;
% Deal with powers of 2 first %
while not odd( n ) do begin
total := total + power;
power := power * 2;
n := n div 2
end while_not_odd_n ;
% Odd prime factors up to the square root %
p := 3;
while ( p * p ) <= n do begin
integer sum;
sum := 1;
power := p;
while n rem p = 0 do begin
sum := sum + power;
power := power * p;
n := n div p
end while_n_rem_p_eq_0 ;
p := p + 2;
total := total * sum
end while_p_x_p_le_n ;
% If n > 1 then it's prime %
if n > 1 then total := total * ( n + 1 );
total
end divisor_sum ;
begin
integer limit;
limit := 100;
write( i_w := 1, s_w := 0, "Sum of divisors for the first ", limit, " positive integers:" );
for n := 1 until limit do begin
if n rem 10 = 1 then write();
writeon( i_w := 4, s_w := 1, divisor_sum( n ) )
end for_n
end
end.- Output:
Sum of divisors for the first 100 positive integers: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
APL
10 10 ⍴ +/∘(⍸0=⍳|⊢)¨⍳100
- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
AppleScript
on sumOfDivisors(n)
if (n < 1) then return 0
set sum to 0
set sqrt to n ^ 0.5
set limit to sqrt div 1
if (limit = sqrt) then
set sum to sum + limit
set limit to limit - 1
end if
repeat with i from 1 to limit
if (n mod i is 0) then set sum to sum + i + n div i
end repeat
return sum
end sumOfDivisors
on task()
set output to {}
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to ""
repeat with i from 0 to 80 by 20
set thisLine to {}
repeat with j from 1 to 20
set end of thisLine to text -4 thru -1 of (" " & sumOfDivisors(i + j))
end repeat
set end of output to thisLine as text
end repeat
set AppleScript's text item delimiters to linefeed
set output to output as text
set AppleScript's text item delimiters to astid
return output
end task
return task()
- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Arturo
loop split.every:10 map 1..100 'x -> sum factors x 'row [
print map row 'r -> pad to :string r 4
]
- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
AWK
# syntax: GAWK -f SUM_OF_DIVISORS.AWK
# converted from Go
BEGIN {
limit = 100
printf("The sums of positive divisors for the first %d positive integers are:\n",limit)
for (i=1; i<=limit; i++) {
printf("%3d ",sum_divisors(i))
if (i % 10 == 0) {
printf("\n")
}
}
exit(0)
}
function sum_divisors(n, ans,i,j,k) {
ans = 0
i = 1
k = (n % 2 == 0) ? 1 : 2
while (i*i <= n) {
if (n % i == 0) {
ans += i
j = n / i
if (j != i) {
ans += j
}
}
i += k
}
return(ans)
}
- Output:
The sums of positive divisors for the first 100 positive integers are: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
BASIC
10 DEFINT A-Z: DATA 100
20 READ M
30 DIM D(M)
40 FOR I=1 TO M
50 FOR J=I TO M STEP I: D(J)=D(J)+I: NEXT
60 PRINT D(I),
70 NEXT
- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
BASIC256
print 1; chr(9);
for n = 2 to 100
p = 1 + n
for i = 2 to n / 2
if n mod i = 0 then p += i
next i
print p; chr(9);
next n
endPureBasic
OpenConsole()
Print("1")
For n.i = 2 To 100
p = 1 + n
For i.i = 2 To n / 2
If Mod(n, i) = 0 : p + i : EndIf
Next i
Print(#TAB$ + Str(p))
Next n
Input()
CloseConsole()QBasic
PRINT 1,
FOR n = 2 TO 100
p = 1 + n
FOR i = 2 TO n / 2
IF n MOD i = 0 THEN p = p + i
NEXT i
PRINT p,
NEXT n
END
True BASIC
PRINT 1,
FOR n = 2 To 100
LET p = 1 + n
FOR i = 2 To n / 2
IF MOD(n, i) = 0 Then LET p = p + i
NEXT i
PRINT p,
NEXT n
END
Yabasic
print 1,
for n = 2 to 100
p = 1 + n
for i = 2 to n / 2
if mod(n, i) = 0 then p = p + i : fi
next i
print p,
next n
end
BCPL
get "libhdr"
manifest $( MAXIMUM = 100 $)
// Calculate sum of divisors of positive integers up to N inclusive
let sumdivs(v, n) be
$( for i=1 to n do v!i := 1 // All numbers are divisible by 1
for i=2 to n do
$( let j = i
while j<=n do
$( v!j := v!j + i // Every multiple of i is divisible by i
j := j + i
$)
$)
$)
// Print sum of divisors from 1 to MAXIMUM
let start() be
$( let divsum = vec MAXIMUM
let col = 0
sumdivs(divsum, MAXIMUM)
for i = 1 to MAXIMUM do
$( writed(divsum!i, 5)
col := col + 1
if col rem 10 = 0 then wrch('*N')
$)
$)- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
C
#include <stdio.h>
// See https://en.wikipedia.org/wiki/Divisor_function
unsigned int divisor_sum(unsigned int n) {
unsigned int total = 1, power = 2;
unsigned int p;
// Deal with powers of 2 first
for (; (n & 1) == 0; power <<= 1, n >>= 1) {
total += power;
}
// Odd prime factors up to the square root
for (p = 3; p * p <= n; p += 2) {
unsigned int sum = 1;
for (power = p; n % p == 0; power *= p, n /= p) {
sum += power;
}
total *= sum;
}
// If n > 1 then it's prime
if (n > 1) {
total *= n + 1;
}
return total;
}
int main() {
const unsigned int limit = 100;
unsigned int n;
printf("Sum of divisors for the first %d positive integers:\n", limit);
for (n = 1; n <= limit; ++n) {
printf("%4d", divisor_sum(n));
if (n % 10 == 0) {
printf("\n");
}
}
return 0;
}
- Output:
Sum of divisors for the first 100 positive integers: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
C++
#include <iomanip>
#include <iostream>
// See https://en.wikipedia.org/wiki/Divisor_function
unsigned int divisor_sum(unsigned int n) {
unsigned int total = 1, power = 2;
// Deal with powers of 2 first
for (; (n & 1) == 0; power <<= 1, n >>= 1)
total += power;
// Odd prime factors up to the square root
for (unsigned int p = 3; p * p <= n; p += 2) {
unsigned int sum = 1;
for (power = p; n % p == 0; power *= p, n /= p)
sum += power;
total *= sum;
}
// If n > 1 then it's prime
if (n > 1)
total *= n + 1;
return total;
}
int main() {
const unsigned int limit = 100;
std::cout << "Sum of divisors for the first " << limit << " positive integers:\n";
for (unsigned int n = 1; n <= limit; ++n) {
std::cout << std::setw(4) << divisor_sum(n);
if (n % 10 == 0)
std::cout << '\n';
}
}
- Output:
Sum of divisors for the first 100 positive integers: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Clojure
(require '[clojure.string :refer [join]])
(require '[clojure.pprint :refer [cl-format]])
(defn divisors [n] (filter #(zero? (rem n %)) (range 1 (inc n))))
(defn display-results [label per-line width nums]
(doall (map println (cons (str "\n" label ":") (list
(join "\n" (map #(join " " %)
(partition-all per-line
(map #(cl-format nil "~v:d" width %) nums)))))))))
(display-results "Tau function - first 100" 20 3
(take 100 (map (comp count divisors) (drop 1 (range)))))
(display-results "Tau numbers – first 100" 10 5
(take 100 (filter #(zero? (rem % (count (divisors %)))) (drop 1 (range)))))
(display-results "Divisor sums – first 100" 20 4
(take 100 (map #(reduce + (divisors %)) (drop 1 (range)))))
(display-results "Divisor products – first 100" 5 16
(take 100 (map #(reduce * (divisors %)) (drop 1 (range)))))
- Output:
Tau function - first 100:
1 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5 2 6 2 6
4 4 2 8 3 4 4 6 2 8 2 6 4 4 4 9 2 4 4 8
2 8 2 6 6 4 2 10 3 6 4 6 2 8 4 8 4 4 2 12
2 4 6 7 4 8 2 6 4 8 2 12 2 4 6 6 4 8 2 10
5 4 2 12 4 4 4 8 2 12 4 6 4 4 4 12 2 6 6 9
Tau numbers – first 100:
1 2 8 9 12 18 24 36 40 56
60 72 80 84 88 96 104 108 128 132
136 152 156 180 184 204 225 228 232 240
248 252 276 288 296 328 344 348 360 372
376 384 396 424 441 444 448 450 468 472
480 488 492 504 516 536 560 564 568 584
600 612 625 632 636 640 664 672 684 708
712 720 732 776 792 804 808 824 828 852
856 864 872 876 880 882 896 904 936 948
972 996 1,016 1,040 1,044 1,048 1,056 1,068 1,089 1,096
Divisor sums – first 100:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42
32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90
42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168
62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186
121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Divisor products – first 100:
1 2 3 8 5
36 7 64 27 100
11 1,728 13 196 225
1,024 17 5,832 19 8,000
441 484 23 331,776 125
676 729 21,952 29 810,000
31 32,768 1,089 1,156 1,225
10,077,696 37 1,444 1,521 2,560,000
41 3,111,696 43 85,184 91,125
2,116 47 254,803,968 343 125,000
2,601 140,608 53 8,503,056 3,025
9,834,496 3,249 3,364 59 46,656,000,000
61 3,844 250,047 2,097,152 4,225
18,974,736 67 314,432 4,761 24,010,000
71 139,314,069,504 73 5,476 421,875
438,976 5,929 37,015,056 79 3,276,800,000
59,049 6,724 83 351,298,031,616 7,225
7,396 7,569 59,969,536 89 531,441,000,000
8,281 778,688 8,649 8,836 9,025
782,757,789,696 97 941,192 970,299 1,000,000,000
CLU
% Calculate sum of divisors of positive integers up to and including N
div_sums = proc (n: int) returns (array[int])
% Every number is at least divisible by 1
ds: array[int] := array[int]$fill(1, n, 1)
for i: int in int$from_to(2, n) do
for j: int in int$from_to_by(i, n, i) do
ds[j] := ds[j] + i % every multiple of i is divisible by i
end
end
return (ds)
end div_sums
% Print sum of divisors from 1 to 100
start_up = proc ()
po: stream := stream$primary_output()
col: int := 0
for i: int in array[int]$elements(div_sums(100)) do
stream$putright(po, int$unparse(i), 5)
col := col + 1
if col // 10 = 0 then stream$putc(po, '\n') end
end
end start_up- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Comal
0010 max#:=100
0020 //
0030 DIM divsum#(max#)
0040 FOR i#:=1 TO max# DO divsum#(i#):=1
0050 FOR i#:=2 TO max# DO FOR j#:=i# TO max# STEP i# DO divsum#(j#):+i#
0060 //
0070 ZONE 5
0080 FOR i#:=1 TO max# DO
0090 PRINT divsum#(i#),
0100 IF i# MOD 10=0 THEN PRINT
0110 ENDFOR i#
0120 END
- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Common Lisp
(format t "~{~a ~}~%"
(loop for a from 1 to 100 collect
(loop for b from 1 to a
when (zerop (rem a b))
sum b)))
- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Cowgol
include "cowgol.coh";
const MAXIMUM := 100;
typedef N is int(0, MAXIMUM+1);
sub print_col(n: N, colsize: uint8) is
var buf: uint8[32];
var nsize := UIToA(n as uint32, 10, &buf[0]) - &buf[0];
while colsize > nsize as uint8 loop
print_char(' ');
colsize := colsize - 1;
end loop;
print(&buf[0]);
end sub;
var divsum: N[MAXIMUM+1];
var i: N := 1;
while i <= MAXIMUM loop
divsum[i] := 1;
i := i + 1;
end loop;
i := 2;
while i <= MAXIMUM loop
var j := i;
while j <= MAXIMUM loop
divsum[j] := divsum[j] + i;
j := j + i;
end loop;
i := i + 1;
end loop;
var col: uint8 := 0;
i := 1;
while i <= MAXIMUM loop
print_col(divsum[i], 5);
col := col + 1;
if col == 10 then
print_nl();
col := 0;
end if;
i := i + 1;
end loop;- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
D
import std.stdio;
// See https://en.wikipedia.org/wiki/Divisor_function
uint divisor_sum(uint n) {
uint total = 1, power = 2;
// Deal with powers of 2 first
for (; (n & 1) == 0; power <<= 1, n >>= 1) {
total += power;
}
// Odd prime factors up to the square root
for (uint p = 3; p * p <= n; p += 2) {
uint sum = 1;
for (power = p; n % p == 0; power *= p, n /= p) {
sum += power;
}
total *= sum;
}
// If n > 1 then it's prime
if (n > 1) {
total *= n + 1;
}
return total;
}
void main() {
immutable limit = 100;
writeln("Sum of divisors for the first ", limit," positive integers:");
for (uint n = 1; n <= limit; ++n) {
writef("%4d", divisor_sum(n));
if (n % 10 == 0) {
writeln;
}
}
}
- Output:
Sum of divisors for the first 100 positive integers: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Delphi
program Sum_of_divisors;
{$APPTYPE CONSOLE}
uses
System.SysUtils;
function DivisorSum(n: Cardinal): Cardinal;
var
total, power, p, sum: Cardinal;
begin
total := 1;
power := 2;
// Deal with powers of 2 first
while (n and 1 = 0) do
begin
inc(total, power);
power := power shl 1;
n := n shr 1;
end;
// Odd prime factors up to the square root
p := 3;
while p * p <= n do
begin
sum := 1;
power := p;
while n mod p = 0 do
begin
inc(sum, power);
power := power * p;
n := n div p;
end;
total := total * sum;
inc(p, 2);
end;
// If n > 1 then it's prime
if n > 1 then
total := total * (n + 1);
Result := total;
end;
begin
const limit = 100;
writeln('Sum of divisors for the first ', limit, ' positive integers:');
for var n := 1 to limit do
begin
Write(divisorSum(n): 8);
if n mod 10 = 0 then
writeln;
end;
{$IFNDEF UNIX} readln; {$ENDIF}
end.
F#
This task uses Extensible Prime Generator (F#).
// Sum of divisors. Nigel Galloway: March 9th., 2021
let sod u=let P=primes32()
let rec fN g=match u%g with 0->g |_->fN(Seq.head P)
let rec fG n i g e l=match n=u,u%l with (true,_)->e*g |(_,0)->fG (n*i) i g (e+l)(l*i) |_->let q=fN(Seq.head P) in fG n q (g*e) 1 q
let n=Seq.head P in fG 1 n 1 1 n
[1..100]|>Seq.iter(sod>>printf "%d "); printfn ""
- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Factor
USING: grouping io math.primes.factors math.ranges prettyprint
sequences ;
"Sum of divisors for the first 100 positive integers:" print
100 [1,b] [ divisors sum ] map 10 group simple-table.
- Output:
Sum of divisors for the first 100 positive integers: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Fermat
Func Sumdiv(n)=sm:=0;for i=1 to n do if Divides(i,n) then sm:=sm+i fi od; sm.
for i=1 to 100 do !!Sumdiv(i) odFOCAL
01.10 S C=0
01.20 F I=1,100;S D(I)=1
01.30 F I=2,100;F J=I,I,100;S D(J)=D(J)+I
01.40 F I=1,100;D 2
01.50 Q
02.10 T %4,D(I)
02.20 S C=C+1
02.30 I (9-C)2.4;R
02.40 T !
02.50 S C=0- Output:
= 1= 3= 4= 7= 6= 12= 8= 15= 13= 18 = 12= 28= 14= 24= 24= 31= 18= 39= 20= 42 = 32= 36= 24= 60= 31= 42= 40= 56= 30= 72 = 32= 63= 48= 54= 48= 91= 38= 60= 56= 90 = 42= 96= 44= 84= 78= 72= 48= 124= 57= 93 = 72= 98= 54= 120= 72= 120= 80= 90= 60= 168 = 62= 96= 104= 127= 84= 144= 68= 126= 96= 144 = 72= 195= 74= 114= 124= 140= 96= 168= 80= 186 = 121= 126= 84= 224= 108= 132= 120= 180= 90= 234 = 112= 168= 128= 144= 120= 252= 98= 171= 156= 217
Forth
: divisor_sum ( n -- n )
1 >r
2
begin
over 2 mod 0=
while
dup r> + >r
2*
swap 2/ swap
repeat
drop
3
begin
2dup dup * >=
while
dup
1 >r
begin
2 pick 2 pick mod 0=
while
dup r> + >r
over * >r
tuck / swap
r>
repeat
2r> * >r
drop
2 +
repeat
drop
dup 1 > if 1+ r> * else drop r> then ;
: print_divisor_sums ( n -- )
." Sum of divisors for the first " dup . ." positive integers:" cr
1+ 1 do
i divisor_sum 4 .r
i 10 mod 0= if cr else space then
loop ;
100 print_divisor_sums
bye
- Output:
Sum of divisors for the first 100 positive integers: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Fortran
program DivSum
implicit none
integer i, j, col, divs(100)
do 10 i=1, 100, 1
10 divs(i) = 1
do 20 i=2, 100, 1
do 20 j=i, 100, i
20 divs(j) = divs(j) + i
col = 0
do 30 i=1, 100, 1
write (*,'(I4)',advance='no') divs(i)
col = col + 1
if (col .eq. 10) then
col = 0
write (*,*)
end if
30 continue
end program
- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
FreeBASIC
dim p as ulongint
print 1,
for n as uinteger = 2 to 100
p = 1+n
for i as uinteger = 2 to n/2
if n mod i = 0 then p += i
next i
print p,
next n- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Frink
for n = 1 to 100
print[sum[allFactors[n]] + " "]- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website.
In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.
Solution
Test case 1. Show the result for the first 100 positive integers
Test case 2. Char
Go
package main
import "fmt"
func sumDivisors(n int) int {
sum := 0
i := 1
k := 2
if n%2 == 0 {
k = 1
}
for i*i <= n {
if n%i == 0 {
sum += i
j := n / i
if j != i {
sum += j
}
}
i += k
}
return sum
}
func main() {
fmt.Println("The sums of positive divisors for the first 100 positive integers are:")
for i := 1; i <= 100; i++ {
fmt.Printf("%3d ", sumDivisors(i))
if i%10 == 0 {
fmt.Println()
}
}
}
- Output:
The sums of positive divisors for the first 100 positive integers are: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
GW-BASIC
5 PRINT 1,
10 FOR N = 2 TO 100
20 P = 1 + N
30 FOR I = 2 TO INT(N/2)
40 IF N MOD I = 0 THEN P = P + I
50 NEXT I
60 PRINT P,
70 NEXT N- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156
217
Haskell
import Data.List.Split (chunksOf)
------------------------- DIVISORS -----------------------
divisors
:: Integral a
=> a -> [a]
divisors n =
((<>) <*> (rest . reverse . fmap (quot n))) $
filter ((0 ==) . rem n) [1 .. root]
where
root = (floor . sqrt . fromIntegral) n
rest
| n == root * root = tail
| otherwise = id
-------------- SUMS AND PRODUCTS OF DIVISORS -------------
main :: IO ()
main =
mapM_
putStrLn
[ "Sums of divisors of [1..100]:"
, test sum
, "Products of divisors of [1..100]:"
, test product
]
test
:: (Show a, Integral a)
=> ([a] -> a) -> String
test f =
let xs = show . f . divisors <$> [1 .. 100]
w = maximum $ length <$> xs
in unlines $ unwords <$> fmap (fmap (justifyRight w ' ')) (chunksOf 5 xs)
justifyRight :: Int -> Char -> String -> String
justifyRight n c = (drop . length) <*> (replicate n c <>)
- Output:
Sums of divisors of [1..100]:
1 3 4 7 6
12 8 15 13 18
12 28 14 24 24
31 18 39 20 42
32 36 24 60 31
42 40 56 30 72
32 63 48 54 48
91 38 60 56 90
42 96 44 84 78
72 48 124 57 93
72 98 54 120 72
120 80 90 60 168
62 96 104 127 84
144 68 126 96 144
72 195 74 114 124
140 96 168 80 186
121 126 84 224 108
132 120 180 90 234
112 168 128 144 120
252 98 171 156 217
Products of divisors of [1..100]:
1 2 3 8 5
36 7 64 27 100
11 1728 13 196 225
1024 17 5832 19 8000
441 484 23 331776 125
676 729 21952 29 810000
31 32768 1089 1156 1225
10077696 37 1444 1521 2560000
41 3111696 43 85184 91125
2116 47 254803968 343 125000
2601 140608 53 8503056 3025
9834496 3249 3364 59 46656000000
61 3844 250047 2097152 4225
18974736 67 314432 4761 24010000
71 139314069504 73 5476 421875
438976 5929 37015056 79 3276800000
59049 6724 83 351298031616 7225
7396 7569 59969536 89 531441000000
8281 778688 8649 8836 9025
782757789696 97 941192 970299 1000000000
J
Brute force:
spd=: {{+/I.0=y|~i.1+y}}"0
spd 1+i.10 10
1 3 4 7 6 12 8 15 13 18
12 28 14 24 24 31 18 39 20 42
32 36 24 60 31 42 40 56 30 72
32 63 48 54 48 91 38 60 56 90
42 96 44 84 78 72 48 124 57 93
72 98 54 120 72 120 80 90 60 168
62 96 104 127 84 144 68 126 96 144
72 195 74 114 124 140 96 168 80 186
121 126 84 224 108 132 120 180 90 234
112 168 128 144 120 252 98 171 156 217
Of course, there are other alternatives.
Java
public class DivisorSum {
private static long divisorSum(long n) {
var total = 1L;
var power = 2L;
// Deal with powers of 2 first
for (; (n & 1) == 0; power <<= 1, n >>= 1) {
total += power;
}
// Odd prime factors up to the square root
for (long p = 3; p * p <= n; p += 2) {
long sum = 1;
for (power = p; n % p == 0; power *= p, n /= p) {
sum += power;
}
total *= sum;
}
// If n > 1 then it's prime
if (n > 1) {
total *= n + 1;
}
return total;
}
public static void main(String[] args) {
final long limit = 100;
System.out.printf("Sum of divisors for the first %d positive integers:%n", limit);
for (long n = 1; n <= limit; ++n) {
System.out.printf("%4d", divisorSum(n));
if (n % 10 == 0) {
System.out.println();
}
}
}
}
- Output:
Sum of divisors for the first 100 positive integers: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
jq
Works with gojq, the Go implementation of jq
Since a "divisors" function is more likely to be generally useful than a "sum of divisors" function, this entry implements the latter in terms of the former.
# divisors as an unsorted stream
def divisors:
if . == 1 then 1
else . as $n
| label $out
| range(1; $n) as $i
| ($i * $i) as $i2
| if $i2 > $n then break $out
else if $i2 == $n then $i
elif ($n % $i) == 0 then $i, ($n/$i)
else empty
end
end
end;
def add(s): reduce s as $x (null; .+$x);
def sum_of_divisors: add(divisors);
# For pretty-printing
def nwise($n):
def n: if length <= $n then . else .[0:$n] , (.[$n:] | n) end;
n;
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
# The task:
[range(1; 101) | sum_of_divisors] | nwise(10) | map(lpad(4)) | join("")- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Julia
using Primes
function sumdivisors(n)
f = [one(n)]
for (p, e) in factor(n)
f = reduce(vcat, [f * p^j for j in 1:e], init = f)
end
return sum(f)
end
for i in 1:100
print(rpad(sumdivisors(i), 5), i % 25 == 0 ? " \n" : "")
end
- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Kotlin
fun divisorSum(n: Long): Long {
var nn = n
var total = 1L
var power = 2L
// Deal with powers of 2 first
while ((nn and 1) == 0L) {
total += power
power = power shl 1
nn = nn shr 1
}
// Odd prime factors up to the square root
var p = 3L
while (p * p <= nn) {
var sum = 1L
power = p
while (nn % p == 0L) {
sum += power
power *= p
nn /= p
}
total *= sum
p += 2
}
// If n > 1 then it's prime
if (nn > 1) {
total *= nn + 1
}
return total
}
fun main() {
val limit = 100L
println("Sum of divisors for the first $limit positive integers:")
for (n in 1..limit) {
print("%4d".format(divisorSum(n)))
if (n % 10 == 0L) {
println()
}
}
}
- Output:
Sum of divisors for the first 100 positive integers: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Lua
...via Algol 68do -- sum the divisors of the first 100 positive integers
-- computes the sum of the divisors of v using the prime factorisation
function divisor_sum( v )
local total, power, n = 1, 2, v
while n % 2 == 0 do -- Deal with powers of 2 first
total = total + power
power = power * 2
n = math.floor( n / 2 )
end
local p = 3 -- Odd prime factors up to the square root
while ( p * p ) <= n do
local sum = 1
power = p
while n % p == 0 do
sum = sum + power
power = power * p
n = math.floor( n / p )
end
p = p + 2
total = total * sum
end
if n > 1 then total = total * ( n + 1 ) end -- If n > 1 then it's prime
return total
end
-- show the first 100 divisor sums
local limit = 100
io.write( "Sum of divisors for the first ", limit, " positive integers:\n" )
for n = 1, limit do
io.write( string.format( " %4d", divisor_sum( n ) ) )
if n % 10 == 0 then io.write( "\n" ) end
end
end
- Output:
Sum of divisors for the first 100 positive integers:
1 3 4 7 6 12 8 15 13 18
12 28 14 24 24 31 18 39 20 42
32 36 24 60 31 42 40 56 30 72
32 63 48 54 48 91 38 60 56 90
42 96 44 84 78 72 48 124 57 93
72 98 54 120 72 120 80 90 60 168
62 96 104 127 84 144 68 126 96 144
72 195 74 114 124 140 96 168 80 186
121 126 84 224 108 132 120 180 90 234
112 168 128 144 120 252 98 171 156 217
MAD
NORMAL MODE IS INTEGER
DIMENSION DIVSUM(100)
THROUGH INIT, FOR I=1, 1, I.G.100
INIT DIVSUM(I) = 1
THROUGH CALC, FOR D=2, 1, D.G.100
THROUGH CALC, FOR M=D, D, M.G.100
CALC DIVSUM(M) = DIVSUM(M) + D
THROUGH SHOW, FOR I=1, 10, I.G.100
SHOW PRINT FORMAT F, DIVSUM(I), DIVSUM(I+1),
0 DIVSUM(I+2), DIVSUM(I+3), DIVSUM(I+4),
1 DIVSUM(I+5), DIVSUM(I+6), DIVSUM(I+7),
2 DIVSUM(I+8), DIVSUM(I+9)
VECTOR VALUES F = $10(I4)*$
END OF PROGRAM- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Mathematica/Wolfram Language
DivisorSigma[1, Range[100]]
- Output:
{1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84, 144, 68, 126, 96, 144, 72, 195, 74, 114, 124, 140, 96, 168, 80, 186, 121, 126, 84, 224, 108, 132, 120, 180, 90, 234, 112, 168, 128, 144, 120, 252, 98, 171, 156, 217}
MiniScript
divisorSum = function(n)
ans = 0
i = 1
while i * i <= n
if n % i == 0 then
ans += i
j = floor(n / i)
if j != i then ans += j
end if
i += 1
end while
return ans
end function
sums = []
for n in range(1, 100)
sums.push(divisorSum(n))
end for
print sums.join(", ")
- Output:
1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84, 144, 68, 126, 96, 144, 72, 195, 74, 114, 124, 140, 96, 168, 80, 186, 121, 126, 84, 224, 108, 132, 120, 180, 90, 234, 112, 168, 128, 144, 120, 252, 98, 171, 156, 217
Nim
import math, strutils
proc divisors(n: Positive): seq[int] =
for d in 1..sqrt(n.toFloat).int:
if n mod d == 0:
result.add d
if n div d != d:
result.add n div d
for n in 1..100:
stdout.write ($sum(n.divisors)).align(3), if (n + 1) mod 10 == 0: '\n' else: ' '
- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156
Pascal
Free Pascal
Brute force version.Checking all divisors up to sqrt(n). More clever is Sum_of_divisors#Delphi.But why not a different version.
Runs with gpc too.//cardinal is 32 or 64 bit depending on OS-System
program Sum_of_divisors;
{$IFDEF WINDOWS}}
{$APPTYPE CONSOLE}
{$ENDIF}
{$IFDEF DELPHI}
uses
System.SysUtils;
{$ENDIF}
function DivisorSum(n: Cardinal): Cardinal;
//check up to i*i= n
var
i,quot,total: Cardinal;
begin
total :=n+1;
i := 2;
repeat
quot := n div i;
//i >= sqrt(n) reached
if quot <= i then
BREAK;
// n mod i = 0
if quot*i = n then
inc(total,i+quot);
inc(i);
until false;
if i*i = n then
inc(total,i);
DivisorSum := total;
end;
const
limit = 100;
var
res,
n : cardinal;
begin
writeln('Sum of divisors for the first ', limit, ' positive integers:');
for n := 1 to limit do
begin
res := divisorSum(n);
Write(res: 4);
if n mod 20 = 0 then
writeln;
end;
{$IFDEF WINDOWS}}
readln;
{$ENDIF}
end.
- Output:
Sum of divisors for the first 100 positive integers: 2 5 4 7 6 15 8 15 13 18 12 32 14 24 24 31 18 39 20 47 32 36 24 60 31 42 40 56 30 78 32 63 48 54 48 91 38 60 56 90 42 103 44 84 78 72 48 124 57 93 72 98 54 120 72 128 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 204 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 244 112 168 128 144 120 252 98 171 156 217
Perl
use strict;
use warnings;
use feature 'say';
use ntheory 'divisor_sum';
my @x;
push @x, scalar divisor_sum($_) for 1..100;
say "Divisor sums - first 100:\n" .
((sprintf "@{['%4d' x 100]}", @x[0..100-1]) =~ s/(.{80})/$1\n/gr);
- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
PARI/GP
vector(100,X,sigma(X))- Output:
[1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84, 144, 68, 126, 96, 144, 72, 195, 74, 114, 124, 140, 96, 168, 80, 186, 121, 126, 84, 224, 108, 132, 120, 180, 90, 234, 112, 168, 128, 144, 120, 252, 98, 171, 156, 217]
Phix
imperative
for i=1 to 100 do printf(1,"%4d",{sum(factors(i,1))}) if remainder(i,10)=0 then puts(1,"\n") end if end for
- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
functional
same output
sequence r = apply(apply(true,factors,{tagset(100),{1}}),sum) puts(1,join_by(apply(true,sprintf,{{"%4d"},r}),1,10,""))
inline assembly
just to show it can be done, not that many would want to, same output
without javascript_semantics for i=1 to 100 do integer res #ilASM {mov edi,[i] mov ecx,1 xor esi,esi cmp edi,ecx je done ::add_divisor add esi,ecx ::next_divisor add ecx,1 mov eax,edi xor edx,edx div ecx cmp eax,ecx jb done je square_root test edx,edx jnz next_divisor add esi,eax jmp add_divisor ::square_root test edx,edx jnz done add esi,eax ::done add esi,edi mov [res],esi } printf(1,"%4d",res) if remainder(i,10)=0 then puts(1,"\n") end if end for
PicoLisp
(de propdiv (N)
(let S 0
(for X N
(and (=0 (% N X)) (inc 'S X)) )
S ) )
(do 10
(do 10
(prin (align 4 (propdiv (inc (0))))) )
(prinl) )- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
PL/M
100H:
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;
DECLARE LIMIT LITERALLY '100';
PRINT$NUMBER: PROCEDURE (N);
DECLARE S (7) BYTE INITIAL (' .....$');
DECLARE N ADDRESS, I BYTE;
I = 6;
DIGIT:
I = I - 1;
S(I) = N MOD 10 + '0';
N = N/10;
IF N>0 THEN GO TO DIGIT;
I = I - 1;
DO WHILE I > 0;
S(I) = ' ';
I = I - 1;
END;
CALL PRINT(.S);
END PRINT$NUMBER;
/* CALCULATE SUMS OF DIVISORS UP TO N INCLUSIVE */
CALC$DIVSUM: PROCEDURE (N, BUF);
DECLARE (I, J, N, BUF, D BASED BUF) ADDRESS;
DO I = 1 TO N;
D(I) = 1;
END;
DO I = 2 TO N;
DO J = I TO N BY I;
D(J) = D(J) + I;
END;
END;
END CALC$DIVSUM;
/* PRINT RESULTS */
DECLARE I ADDRESS;
DECLARE COL BYTE INITIAL (0);
DECLARE DIVS (LIMIT) ADDRESS;
CALL CALC$DIVSUM(LIMIT, .DIVS);
DO I = 1 TO LIMIT;
CALL PRINT$NUMBER(DIVS(I));
COL = COL + 1;
IF COL = 10 THEN DO;
CALL PRINT(.(13,10,'$'));
COL = 0;
END;
END;
CALL EXIT;
EOF- Output:
1 3 4 7 6 12 8 15 13 18
12 28 14 24 24 31 18 39 20 42
32 36 24 60 31 42 40 56 30 72
32 63 48 54 48 91 38 60 56 90
42 96 44 84 78 72 48 124 57 93
72 98 54 120 72 120 80 90 60 168
62 96 104 127 84 144 68 126 96 144
72 195 74 114 124 140 96 168 80 186
121 126 84 224 108 132 120 180 90 234
112 168 128 144 120 252 98 171 156 217
Python
Using prime factorization
def factorize(n):
assert(isinstance(n, int))
if n < 0:
n = -n
if n < 2:
return
k = 0
while 0 == n%2:
k += 1
n //= 2
if 0 < k:
yield (2,k)
p = 3
while p*p <= n:
k = 0
while 0 == n%p:
k += 1
n //= p
if 0 < k:
yield (p,k)
p += 2
if 1 < n:
yield (n,1)
def sum_of_divisors(n):
assert(n != 0)
ans = 1
for (p,k) in factorize(n):
ans *= (pow(p,k+1) - 1)//(p-1)
return ans
if __name__ == "__main__":
print([sum_of_divisors(n) for n in range(1,101)])
Finding divisors efficiently
def sum_of_divisors(n):
assert(isinstance(n, int) and 0 < n)
ans, i, j = 0, 1, 1
while i*i <= n:
if 0 == n%i:
ans += i
j = n//i
if j != i:
ans += j
i += 1
return ans
if __name__ == "__main__":
print([sum_of_divisors(n) for n in range(1,101)])
- Output:
[1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84, 144, 68, 126, 96, 144, 72, 195, 74, 114, 124, 140, 96, 168, 80, 186, 121, 126, 84, 224, 108, 132, 120, 180, 90, 234, 112, 168, 128, 144, 120, 252, 98, 171, 156, 217]
Choosing the right abstraction
This is really an exercise in defining a divisors function, and the only difference between the suggested Sum and Product draft tasks boils down to two trivial morphemes:
reduce(add, divisors(n), 0) vs reduce(mul, divisors(n), 1)
The goal of Rosetta code (see the landing page) is to provide contrastive insight (rather than comprehensive coverage of homework questions :-). Perhaps the scope for contrastive insight in the matter of divisors is already exhausted by the trivially different Proper divisors task.
'''Sums and products of divisors'''
from math import floor, sqrt
from functools import reduce
from operator import add, mul
# divisors :: Int -> [Int]
def divisors(n):
'''List of all divisors of n including n itself.
'''
root = floor(sqrt(n))
lows = [x for x in range(1, 1 + root) if 0 == n % x]
return lows + [n // x for x in reversed(lows)][
(1 if n == (root * root) else 0):
]
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Sums and products of divisors for each integer in range [1..50]
'''
print('Products of divisors:')
for n in range(1, 1 + 50):
print(n, '->', reduce(mul, divisors(n), 1))
print('Sums of divisors:')
for n in range(1, 1 + 100):
print(n, '->', reduce(add, divisors(n), 0))
# MAIN ---
if __name__ == '__main__':
main()
Quackery
factors is defined at Factors of an integer#Quackery.
[ 0 swap factors witheach + ] is sum-of-divisors
[] []
100 times
[ i^ 1+ sum-of-divisors join ]
witheach [ number$ nested join ]
72 wrap$- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
R
This only takes one line.
sapply(1:100, function(n) sum(c(Filter(function(x) n %% x == 0, seq_len(n %/% 2)), n)))Racket
#lang racket/base
(require math/number-theory)
(define (sum-of-divisors n) (apply + (divisors n)))
(displayln (for/list ((n (in-range 1 101))) (sum-of-divisors n)))
- Output:
(1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217)
Raku
Yet more tasks that are tiny variations of each other. Tau function, Tau number, Sum of divisors and Product of divisors all use code with minimal changes. What the heck, post 'em all.
use Prime::Factor:ver<0.3.0+>;
use Lingua::EN::Numbers;
say "\nTau function - first 100:\n", # ID
(1..*).map({ +.&divisors })[^100]\ # the task
.batch(20)».fmt("%3d").join("\n"); # display formatting
say "\nTau numbers - first 100:\n", # ID
(1..*).grep({ $_ %% +.&divisors })[^100]\ # the task
.batch(10)».&comma».fmt("%5s").join("\n"); # display formatting
say "\nDivisor sums - first 100:\n", # ID
(1..*).map({ [+] .&divisors })[^100]\ # the task
.batch(20)».fmt("%4d").join("\n"); # display formatting
say "\nDivisor products - first 100:\n", # ID
(1..*).map({ [×] .&divisors })[^100]\ # the task
.batch(5)».&comma».fmt("%16s").join("\n"); # display formatting
- Output:
Tau function - first 100:
1 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5 2 6 2 6
4 4 2 8 3 4 4 6 2 8 2 6 4 4 4 9 2 4 4 8
2 8 2 6 6 4 2 10 3 6 4 6 2 8 4 8 4 4 2 12
2 4 6 7 4 8 2 6 4 8 2 12 2 4 6 6 4 8 2 10
5 4 2 12 4 4 4 8 2 12 4 6 4 4 4 12 2 6 6 9
Tau numbers - first 100:
1 2 8 9 12 18 24 36 40 56
60 72 80 84 88 96 104 108 128 132
136 152 156 180 184 204 225 228 232 240
248 252 276 288 296 328 344 348 360 372
376 384 396 424 441 444 448 450 468 472
480 488 492 504 516 536 560 564 568 584
600 612 625 632 636 640 664 672 684 708
712 720 732 776 792 804 808 824 828 852
856 864 872 876 880 882 896 904 936 948
972 996 1,016 1,040 1,044 1,048 1,056 1,068 1,089 1,096
Divisor sums - first 100:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42
32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90
42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168
62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186
121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Divisor products - first 100:
1 2 3 8 5
36 7 64 27 100
11 1,728 13 196 225
1,024 17 5,832 19 8,000
441 484 23 331,776 125
676 729 21,952 29 810,000
31 32,768 1,089 1,156 1,225
10,077,696 37 1,444 1,521 2,560,000
41 3,111,696 43 85,184 91,125
2,116 47 254,803,968 343 125,000
2,601 140,608 53 8,503,056 3,025
9,834,496 3,249 3,364 59 46,656,000,000
61 3,844 250,047 2,097,152 4,225
18,974,736 67 314,432 4,761 24,010,000
71 139,314,069,504 73 5,476 421,875
438,976 5,929 37,015,056 79 3,276,800,000
59,049 6,724 83 351,298,031,616 7,225
7,396 7,569 59,969,536 89 531,441,000,000
8,281 778,688 8,649 8,836 9,025
782,757,789,696 97 941,192 970,299 1,000,000,000
REXX
/*REXX program displays the first N sum of divisors (shown in a columnar format). */
parse arg n cols . /*obtain optional argument from the CL.*/
if n=='' | n=="," then n= 100 /*Not specified? Then use the default.*/
if cols=='' | cols=="," then cols= 10 /* " " " " " " */
say ' index │'center("sum of divisors", 102) /*display the title for the column #s. */
say '───────┼'center("" , 102,'─') /* " " separator for the title. */
w= 10 /*W: used to align 1st output column. */
$=; idx= 1 /*$: the output list, shown in columns*/
do j=1 for N /*process N positive integers. */
$= $ || right( commas( sigma(j) ), w) /*add a sigma (sum) to the output list.*/
if j//cols\==0 then iterate /*Not a multiple of cols? Don't display*/
say center(idx, 7)'│' $ /*display partial list to the terminal.*/
idx= idx + cols /*bump the index number for the output.*/
$= /*start with a blank line for next line*/
end /*j*/
if $\=='' then say center(idx, 7)'│' $ /*any residuals sums left to display? */
say '───────┴'center("" , 102,'─') /* " " foot separator for data. */
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
sigma: procedure; parse arg x; if x==1 then return 1; odd=x // 2 /* // ◄──remainder.*/
s= 1 + x /* [↓] only use EVEN or ODD integers.*/
do k=2+odd by 1+odd while k*k<x /*divide by all integers up to √x. */
if x//k==0 then s= s + k + x % k /*add the two divisors to (sigma) sum. */
end /*k*/ /* [↑] % is the REXX integer division*/
if k*k==x then return s + k /*Was X a square? If so, add √ x */
return s /*return (sigma) sum of the divisors. */
- output when using the default input:
index │ sum of divisors ───────┼────────────────────────────────────────────────────────────────────────────────────────────────────── 1 │ 1 3 4 7 6 12 8 15 13 18 11 │ 12 28 14 24 24 31 18 39 20 42 21 │ 32 36 24 60 31 42 40 56 30 72 31 │ 32 63 48 54 48 91 38 60 56 90 41 │ 42 96 44 84 78 72 48 124 57 93 51 │ 72 98 54 120 72 120 80 90 60 168 61 │ 62 96 104 127 84 144 68 126 96 144 71 │ 72 195 74 114 124 140 96 168 80 186 81 │ 121 126 84 224 108 132 120 180 90 234 91 │ 112 168 128 144 120 252 98 171 156 217 ───────┴──────────────────────────────────────────────────────────────────────────────────────────────────────
Ring
see "the sums of divisors for 100 integers:" + nl
num = 0
for n = 1 to 100
sum = 0
for m = 1 to n
if n%m = 0
sum = sum + m
ok
next
num = num + 1
if num%10 = 1
see nl
ok
see "" + sum + " "
nextOutput:
the sums of divisors for 100 integers: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
RPL
| RPL code | Comment |
|---|---|
≪ → n
≪ 0
1 n √ FOR ii
IF n ii MOD NOT THEN
ii +
n ii / FLOOR
IF DUP ii ≠
THEN + ELSE DROP END
END NEXT
≫ ≫ '∑DIV' STO
|
∑DIV ( n -- sum_of_divisors )
ans = 0
while i*i <= n:
if 0 == n%i:
ans += i
j = n//i
if j != i:
ans += j
i += 1
return ans
|
- Input:
≪ { } 1 100 FOR j j ∑DIV + NEXT ≫ EVAL
- Output:
1: { 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217 }
Ruby
def divisor_sum(n)
total = 1
power = 2
# Deal with powers of 2 first
while (n & 1) == 0
total = total + power
power = power << 1
n = n >> 1
end
# Odd prime factors up to the square root
p = 3
while p * p <= n
sum = 1
power = p
while n % p == 0
sum = sum + power
power = power * p
n = (n / p).floor
end
total = total * sum
p = p + 2
end
# If n > 1 then it's prime
if n > 1 then
total = total * (n + 1)
end
return total
end
LIMIT = 100
print "Sum of divisors for the first ", LIMIT, " positive integers:\n"
for n in 1 .. LIMIT
print "%4d" % [divisor_sum(n)]
if n % 10 == 0 then
print "\n"
end
end
- Output:
Sum of divisors for the first 100 positive integers: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Sidef
1..100 -> map { .sigma }.say
- Output:
[1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84, 144, 68, 126, 96, 144, 72, 195, 74, 114, 124, 140, 96, 168, 80, 186, 121, 126, 84, 224, 108, 132, 120, 180, 90, 234, 112, 168, 128, 144, 120, 252, 98, 171, 156, 217]
Tiny BASIC
PRINT 1
LET N = 1
10 LET N = N + 1
LET S = 1 + N
LET I = 1
20 LET I = I + 1
IF I > N/2 THEN GOTO 30
IF (N/I)*I = N THEN LET S = S + I
GOTO 20
30 PRINT S
IF N < 100 THEN GOTO 10
ENDVerilog
module main;
integer n, p, i;
initial begin
$write("1");
for(n=2; n<=100; n=n+1) begin
p = 1 + n;
for(i=2; i<=n/2; i=i+1) if(n % i == 0) p = p + i;
$write(p);
end
$finish ;
end
endmodule
VTL-2
10 C=0
20 M=100
30 I=1
40 :I)=0
50 I=I+1
60 #=M>I*40
70 I=1
80 J=I
90 :J)=:J)+I
100 J=J+I
110 #=M>J*90
120 ?=:I)
130 $=9
140 C=C+1
150 #=C/10*0+0<%*170
160 ?=""
170 I=I+1
180 #=M>I*80- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
Wren
import "/math" for Int, Nums
import "/fmt" for Fmt
System.print("The sums of positive divisors for the first 100 positive integers are:")
for (i in 1..100) {
Fmt.write("$3d ", Nums.sum(Int.divisors(i)))
if (i % 10 == 0) System.print()
}- Output:
The sums of positive divisors for the first 100 positive integers are: 1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
XPL0
func SumDiv(N); \Return sum of divisors of N
int N, Sum, Div;
[Sum:= 0;
for Div:= 1 to N do
if rem(N/Div) = 0 then
Sum:= Sum + Div;
return Sum;
];
int C, N;
[C:= 0;
for N:= 1 to 100 do
[IntOut(0, SumDiv(N));
C:= C+1;
if rem(C/10) then ChOut(0, 9\tab\) else CrLf(0)];
]- Output:
1 3 4 7 6 12 8 15 13 18 12 28 14 24 24 31 18 39 20 42 32 36 24 60 31 42 40 56 30 72 32 63 48 54 48 91 38 60 56 90 42 96 44 84 78 72 48 124 57 93 72 98 54 120 72 120 80 90 60 168 62 96 104 127 84 144 68 126 96 144 72 195 74 114 124 140 96 168 80 186 121 126 84 224 108 132 120 180 90 234 112 168 128 144 120 252 98 171 156 217
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