Special divisors
(Redirected from Special Divisors)
Special 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.
- Task
Numbers n such that reverse(d) divides reverse(n) for all divisors d of n, where n < 200
Action!
PROC CalcDivisors(INT x INT ARRAY div INT POINTER count)
INT i
count^=0
FOR i=1 TO x/2
DO
IF x MOD i=0 THEN
div(count^)=i
count^==+1
FI
OD
RETURN
INT FUNC Reverse(INT x)
INT res
res=0
WHILE x#0
DO
res==*10
res==+x MOD 10
x==/10
OD
RETURN (res)
BYTE FUNC IsSpecial(INT x)
INT ARRAY divisors(100)
INT count,i,rev,revd
CalcDivisors(x,divisors,@count)
rev=Reverse(x)
FOR i=0 TO count-1
DO
revd=Reverse(divisors(i))
IF rev MOD revd#0 THEN
RETURN (0)
FI
OD
RETURN (1)
PROC Main()
INT i
FOR i=1 TO 199
DO
IF IsSpecial(i) THEN
PrintI(i) Put(32)
FI
OD
RETURN- Output:
Screenshot from Atari 8-bit computer
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
ALGOL 68
BEGIN # find numbers where reverse(d) divides reverse(n) for all divisors d #
# of n #
# returns n with the digits reversed #
OP REVERSE = ( INT n )INT:
BEGIN
INT reverse := 0;
INT v := ABS n;
WHILE v > 0 DO
reverse *:= 10 +:= v MOD 10;
v OVERAB 10
OD;
reverse * SIGN n
END # REVERSE # ;
# find the numbers up to 200 #
INT rd count := 0;
FOR n TO 199 DO
INT reverse n = REVERSE n;
BOOL reverse divisor := TRUE;
FOR d FROM 2 TO n OVER 2 WHILE reverse divisor DO
IF n MOD d = 0 THEN
# have a divisor of n #
reverse divisor := reverse n MOD REVERSE d = 0
FI
OD;
IF reverse divisor THEN
# all the divisors of n reversed divide n reversed #
print( ( " ", whole( n, -3 ) ) );
IF ( rd count +:= 1 ) MOD 10 = 0 THEN print( ( newline ) ) FI
FI
OD;
print( ( newline, "Found ", whole( rd count, 0 ), " ""special divisors"" below 200", newline ) )
END- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 Found 72 "special divisors" below 200
ALGOL W
begin % find numbers where reverse(d) divides reverse(n) for all divisors d %
% of n %
% returns n with the digits reversed %
integer procedure reverse ( integer value n ) ;
begin
integer r, v;
r := 0;
v := abs n;
while v > 0 do begin
r := ( r * 10 ) + ( v rem 10 );
v := v div 10
end while_v_gt_0 ;
if n < 0 then - r else r
end reverse ;
% find the numbers up to 200 %
integer rdCount;
rdCount := 0;
for n := 1 until 199 do begin
integer reverseN, d, maxD;
logical reverseDivisor;
reverseN := reverse( n );
reverseDivisor := true;
d := 1;
maxD := n div 2;
while begin
d := d + 1;
d <= maxD and reverseDivisor
end
do begin
if n rem d = 0 then begin
% have a divisor of n %
reverseDivisor := reverseN rem reverse( d ) = 0
end if_n_rem_d_eq_0
end while_d_le_maxD_and_reverseDivisor ;
if reverseDivisor then begin
% all the divisors of n reversed divide n reversed %
writeon( i_w := 3, s_w := 0, " ", n );
rdCount := rdCount + 1;
if rdCount rem 10 = 0 then write()
end if_reverseDivisor
end for_n ;
write( i_w := 1, s_w := 0, "Found ", rdCount, " ""special divisors"" below 200" )
end.- Output:
Same as the Algol 68 sample.
APL
(⊢(/⍨)(0∧.=(⍎⌽∘⍕)¨∘(⍸0=⍳|⊢)|(⍎⌽∘⍕))¨) ⍳200
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47
53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101
103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169
173 179 181 187 191 193 197 199
AppleScript
on factors(n)
set output to {}
if (n > 0) 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 1 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
end if
return output
end factors
on reversedIntVal(n, base)
set r to n mod base as integer
set n to n div base
repeat until (n = 0)
set r to r * base + n mod base
set n to n div base
end repeat
return r
end reversedIntVal
on hasSpecialDivisors(n, base)
set divisors to factors(n)
if (divisors is {}) then return false
set r to reversedIntVal(n, base)
repeat with d in divisors
if (r mod (reversedIntVal(d, base)) > 0) then return false
end repeat
return true
end hasSpecialDivisors
local output, base, n
set output to {}
set base to 10
repeat with n from 1 to 199
if (hasSpecialDivisors(n, base)) then set end of output to n
end repeat
return {|count|:(count output), finds:output}
- Output:
{|count|:72, finds:{1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 19, 22, 23, 26, 27, 29, 31, 33, 37, 39, 41, 43, 44, 46, 47, 53, 55, 59, 61, 62, 66, 67, 69, 71, 73, 77, 79, 82, 83, 86, 88, 89, 93, 97, 99, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199}}
Arturo
reversed: function [x]->
to :integer join to [:string] reverse digits x
specialDivisors: select 1..200 'n ->
every? factors n 'd ->
zero? (reversed n) % reversed d
loop split.every: 9 specialDivisors 'x ->
print map x 's -> pad to :string s 4
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
BASIC
10 DEFINT A-Z
20 FOR I=1 TO 199
30 J=I: X=0
40 IF J>0 THEN X=X*10+J MOD 10: J=J\10: GOTO 40
50 FOR J=1 TO I\2
60 IF I MOD J GOTO 100
70 K=J: Y=0
80 IF K>0 THEN Y=Y*10+K MOD 10: K=K\10: GOTO 80
90 IF X MOD Y GOTO 120
100 NEXT J
110 PRINT I,
120 NEXT I
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
BASIC256
c = 0
for n = 1 to 200
u = reverse(n)
s = true
for d = 1 to n
if n mod d = 0 then
b = reverse(d)
if u mod b <> 0 then s = false
end if
next d
if s then c += 1 : print n; chr(9);
next n
print
print "Found "; c; " special divisors."
end
function reverse(n)
u = 0
while n
u = u * 10 + n mod 10
n = n \ 10
end while
return u
end function- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 Found 72 special divisors.
BCPL
get "libhdr"
let reverse(n) = valof
$( let r = 0
while n > 0
$( r := r*10 + n rem 10
n := n/10
$)
resultis r
$)
let special(n) = valof
$( let r = reverse(n)
for d = 1 to n/2
if n rem d = 0 & r rem reverse(d) ~= 0
resultis false
resultis true
$)
let start() be
$( let c = 0
for n = 1 to 199
if special(n)
$( writed(n,4)
c := c + 1
if c = 10
$( wrch('*N')
c := 0
$)
$)
wrch('*N')
$)- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
C
#include <stdbool.h>
#include <stdio.h>
int reverse(int n) {
int result = 0;
while (n > 0) {
result = 10 * result + n % 10;
n /= 10;
}
return result;
}
int main() {
const int limit1 = 200;
int row = 0;
int num = 0;
int n;
for (n = 1; n < limit1; n++) {
bool flag = true;
int revNum = reverse(n);
int m;
for (m = 1; m < n / 2; m++) {
int revDiv = reverse(m);
if (n % m == 0) {
if (revNum % revDiv == 0) {
flag = true;
} else {
flag = false;
break;
}
}
}
if (flag) {
num++;
row++;
printf("%4d ", n);
if (row % 10 == 0) {
printf("\n");
}
}
}
printf("\n\nFound %d special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200\n", num);
return 0;
}
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 Found 72 special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200
C++
#include <iostream>
#include <iomanip>
#include <vector>
using uint = unsigned int;
std::vector<uint> divisors(uint n) {
std::vector<uint> divs;
for (uint d=1; d<=n/2; d++) {
if (n % d == 0) divs.push_back(d);
}
return divs;
}
uint reverse(uint n) {
uint r;
for (r = 0; n; n /= 10) r = (r*10) + (n%10);
return r;
}
bool special(uint n) {
for (uint d : divisors(n))
if (reverse(n) % reverse(d) != 0) return false;
return true;
}
int main() {
for (uint n=1, c=0; n < 200; n++) {
if (special(n)) {
std::cout << std::setw(4) << n;
if (++c == 10) {
c = 0;
std::cout << std::endl;
}
}
}
std::cout << std::endl;
return 0;
}
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
C#
using System;
namespace SpecialDivisors {
class Program {
static int Reverse(int n) {
int result = 0;
while (n > 0) {
result = 10 * result + n % 10;
n /= 10;
}
return result;
}
static void Main() {
const int LIMIT = 200;
int row = 0;
int num = 0;
for (int n = 1; n < LIMIT; n++) {
bool flag = true;
int revNum = Reverse(n);
for (int m = 1; m < n / 2; m++) {
int revDiv = Reverse(m);
if (n % m == 0) {
if (revNum % revDiv == 0) {
flag = true;
} else {
flag = false;
break;
}
}
}
if (flag) {
num++;
row++;
Console.Write("{0,4}", n);
if (row % 10 == 0) {
Console.WriteLine();
}
}
}
Console.WriteLine();
Console.WriteLine();
Console.WriteLine("Found {0} special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200", num);
}
}
}
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 Found 72 special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200
CLU
reverse = proc (n: int) returns (int)
r: int := 0
while n>0 do
r := r*10 + n//10
n := n/10
end
return(r)
end reverse
special = proc (n: int) returns (bool)
r: int := reverse(n)
for d: int in int$from_to(1,n/2) do
if n//d=0 & r//reverse(d)~=0 then
return(false)
end
end
return(true)
end special
start_up = proc ()
po: stream := stream$primary_output()
c: int := 0
for n: int in int$from_to(1,199) do
if special(n) then
stream$putright(po, int$unparse(n), 4)
c := c+1
if c=10 then
stream$putl(po, "")
c := 0
end
end
end
end start_up- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
COBOL
IDENTIFICATION DIVISION.
PROGRAM-ID. SPECIAL-DIVISORS.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 VARIABLES.
02 CANDIDATE PIC 999.
02 CAND-REV PIC 999.
02 REVERSE PIC 999.
02 REV-DIGITS REDEFINES REVERSE PIC 9 OCCURS 3 TIMES.
02 DIVMAX PIC 999.
02 DIVISOR PIC 999.
02 DIVRSLT PIC 999V999.
02 FILLER REDEFINES DIVRSLT.
03 FILLER PIC 999.
03 FILLER PIC 999.
88 DIVISIBLE VALUE 0.
02 TEMP PIC 9.
02 RD PIC 9 COMP.
02 STATUS-FLAG PIC X.
88 OK VALUE 'Y'.
02 SPECIAL-N PIC ZZ9.
PROCEDURE DIVISION.
BEGIN.
PERFORM CHECK-SPECIAL-DIVISOR
VARYING CANDIDATE FROM 1 BY 1
UNTIL CANDIDATE IS EQUAL TO 200.
STOP RUN.
CHECK-SPECIAL-DIVISOR.
MOVE CANDIDATE TO REVERSE.
PERFORM REVERSE-NUMBER.
MOVE REVERSE TO CAND-REV.
DIVIDE CANDIDATE BY 2 GIVING DIVMAX.
MOVE 'Y' TO STATUS-FLAG.
PERFORM TRY-DIVISOR
VARYING DIVISOR FROM 1 BY 1
UNTIL DIVISOR IS GREATER THAN DIVMAX.
IF OK
MOVE CANDIDATE TO SPECIAL-N
DISPLAY SPECIAL-N.
TRY-DIVISOR.
IF OK
DIVIDE CANDIDATE BY DIVISOR GIVING DIVRSLT
IF DIVISIBLE
MOVE DIVISOR TO REVERSE
PERFORM REVERSE-NUMBER
DIVIDE CAND-REV BY REVERSE GIVING DIVRSLT
IF NOT DIVISIBLE MOVE 'N' TO STATUS-FLAG.
REVERSE-NUMBER.
SET RD TO 1.
INSPECT REVERSE TALLYING RD FOR LEADING '0'.
MOVE REV-DIGITS(RD) TO TEMP.
MOVE REV-DIGITS(3) TO REV-DIGITS(RD).
MOVE TEMP TO REV-DIGITS(3).
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Cowgol
include "cowgol.coh";
const MAXIMUM := 200;
typedef N is int(0, MAXIMUM);
sub reverse(n: N): (r: N) is
r := 0;
while n != 0 loop
r := r*10 + n%10;
n := n/10;
end loop;
end sub;
sub special(n: N): (r: uint8) is
r := 0;
var revn := reverse(n);
var dsor: N := 1;
while dsor <= n/2 loop
if n % dsor == 0 and revn % reverse(dsor) != 0 then
return;
end if;
dsor := dsor + 1;
end loop;
r := 1;
end sub;
var n: N := 1;
while n < MAXIMUM loop
if special(n) != 0 then
print_i32(n as uint32);
print_nl();
end if;
n := n + 1;
end loop;- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199
Delphi
program Special_Divisors;
{$IFDEF FPC}
{$MODE DELPHI}
uses
SysUtils,
StrUtils;
{$ELSE}
{$APPTYPE CONSOLE}
uses
System.SysUtils,
System.StrUtils;
{$ENDIF}
const
limit1 = 200;
var
row, num, revNum, revDiv: Integer;
flag: boolean;
procedure Main();
var
n,m: NativeUint;
begin
writeln('Working...'#10);
row := 0;
num := 0;
for n := 1 to limit1 do
begin
flag := True;
revNum := reversestring(n.ToString).ToInteger;
for m := 1 to n div 2 do
begin
revDiv := reversestring(m.ToString).ToInteger;
if n mod m = 0 then
if revNum mod revDiv = 0 then
flag := True
else
begin
flag := False;
Break;
end;
end;
if flag then
begin
inc(num);
inc(row);
write(n: 4);
if row mod 10 = 0 then
Writeln;
end;
end;
writeln(#10#10'Found ', num,
' special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200');
writeln('Done...');
end;
begin
Main;
{$IFNDEF UNIX} readln; {$ENDIF}
end.
- Output:
Working... 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 Found 72 special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200 Done...
Factor
USING: grouping kernel math.functions math.parser
math.primes.factors math.ranges prettyprint sequences ;
: reverse-number ( n -- reversed ) 10 >base reverse dec> ;
: special? ( n -- ? )
[ reverse-number ] [ divisors ] bi
[ reverse-number divisor? ] with all? ;
200 [1..b] [ special? ] filter 18 group simple-table.
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Forth
: reverse ( n -- n )
0 >r
begin
dup 0 >
while
10 /mod swap
r> 10 * + >r
repeat
drop r> ;
: special? ( n -- ? )
dup reverse >r
2
begin
2dup dup * >=
while
2dup mod 0= if
dup reverse r@ swap mod 0 <> if
rdrop 2drop false exit
then
2dup / dup 2 pick <> if
reverse r@ swap mod 0 <> if
rdrop 2drop false exit
then
else
drop
then
then
1+
repeat
rdrop 2drop true ;
: main
0
200 1 do
i special? if
i 3 .r
1+
dup 10 mod 0= if cr else space then
then
loop cr
. ." numbers found." cr ;
main
bye
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 72 numbers found.
FreeBASIC
function reverse(n as integer) as integer
dim as integer u = 0
while n
u = 10*u + n mod 10
n\=10
wend
return u
end function
dim as integer n, u, d, b
dim as boolean s
for n = 1 to 200
u = reverse(n)
s = true
for d = 1 to n
if n mod d = 0 then
b = reverse(d)
if u mod b <> 0 then s = false
end if
next d
if s then print using "### ";n;
next nGo
package main
import (
"fmt"
"rcu"
)
func reversed(n int) int {
rev := 0
for n > 0 {
rev = rev*10 + n%10
n = n / 10
}
return rev
}
func main() {
var special []int
for n := 1; n < 200; n++ {
divs := rcu.Divisors(n)
revN := reversed(n)
all := true
for _, d := range divs {
if revN%reversed(d) != 0 {
all = false
break
}
}
if all {
special = append(special, n)
}
}
fmt.Println("Special divisors in the range 0..199:")
for i, n := range special {
fmt.Printf("%3d ", n)
if (i+1)%12 == 0 {
fmt.Println()
}
}
fmt.Printf("\n%d special divisors found.\n", len(special))
}
- Output:
Special divisors in the range 0..199: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 72 special divisors found.
J
([#~([:*./0=|.&.":"0@>:@I.@(0=>:@i.|])||.&.":)"0)>:i.200
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
jq
Works with gojq, the Go implementation of jq
# 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 is_special_divisor:
def reverse_number: tostring|explode|reverse|implode|tonumber;
reverse_number as $nreverse
| all(divisors; $nreverse % reverse_number == 0);
range(1;200) | select(is_special_divisor)- Output:
A stream of numbers as shown elsewhere on this page.
Julia
using Primes
function divisors(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 f[1:end-1]
end
function isspecialdivisor(n)::Bool
isprime(n) && return true
nreverse = evalpoly(10, reverse(digits(n)))
for d in divisors(n)
dreverse = evalpoly(10, reverse(digits(d)))
!(nreverse ÷ dreverse ≈ nreverse / dreverse) && return false
end
return true
end
const specials = filter(isspecialdivisor, 1:200)
foreach(p -> print(rpad(p[2], 4), p[1] % 18 == 0 ? "\n" : ""), enumerate(specials))
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
MAD
NORMAL MODE IS INTEGER
INTERNAL FUNCTION(X)
ENTRY TO RVRSE.
XR = X
RR = 0
LOOP WHENEVER XR.E.0, FUNCTION RETURN RR
XD = XR/10
RR = RR*10 + XR-XD*10
XR = XD
TRANSFER TO LOOP
END OF FUNCTION
THROUGH CAND, FOR N=1, 1, N.GE.200
RN = RVRSE.(N)
THROUGH DIVS, FOR D=1, 1, D.G.N/2
RD = RVRSE.(D)
DIVS WHENEVER N/D*D.E.N .AND. RN/RD*RD.NE.RN, TRANSFER TO CAND
PRINT FORMAT FMT,N
CAND CONTINUE
VECTOR VALUES FMT = $I4*$
END OF PROGRAM- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Mathematica/Wolfram Language
SpecialDivisorQ[n_Integer] := AllTrue[Divisors[n], Divisible[IntegerReverse[n], IntegerReverse[#]] &]
Select[Range[199], SpecialDivisorQ]
Length[%]
- Output:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 19, 22, 23, 26, 27, 29, 31, 33, 37, 39, 41, 43, 44, 46, 47, 53, 55, 59, 61, 62, 66, 67, 69, 71, 73, 77, 79, 82, 83, 86, 88, 89, 93, 97, 99, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199}
72
Modula-2
MODULE SpecialDivisors;
FROM InOut IMPORT WriteCard, WriteLn;
CONST Max = 200;
VAR n, col: CARDINAL;
PROCEDURE Reverse(n: CARDINAL): CARDINAL;
VAR result: CARDINAL;
BEGIN
result := 0;
WHILE n > 0 DO
result := result*10 + n MOD 10;
n := n DIV 10;
END;
RETURN result;
END Reverse;
PROCEDURE Special(n: CARDINAL): BOOLEAN;
VAR reverse, divisor: CARDINAL;
BEGIN
reverse := Reverse(n);
FOR divisor := 1 TO n DIV 2 DO
IF (n MOD divisor = 0) AND (reverse MOD Reverse(divisor) # 0) THEN
RETURN FALSE;
END;
END;
RETURN TRUE;
END Special;
BEGIN
col := 0;
FOR n := 1 TO Max DO
IF Special(n) THEN
WriteCard(n, 4);
col := col + 1;
IF col MOD 10 = 0 THEN
WriteLn();
END;
END;
END;
WriteLn();
END SpecialDivisors.
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Nim
import strutils
func reversed(n: Positive): int =
var n = n.int
while n != 0:
result = 10 * result + n mod 10
n = n div 10
func divisors(n: Positive): seq[int] =
result = @[1, n]
var d = 2
while d * d <= n:
if n mod d == 0:
result.add d
if d * d != n:
result.add n div d
inc d
var count = 0
for n in 1..<200:
let revn = reversed(n)
block check:
for d in divisors(n):
if revn mod reversed(d) != 0:
break check
inc count
stdout.write ($n).align(3), if count mod 12 == 0: '\n' else: ' '
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Pascal
see http://rosettacode.org/wiki/Special_Divisors#Delphi%7CDelphi
Perl
use strict;
use warnings;
use feature 'say';
use ntheory 'divisors';
my @sd;
for my $n (1..199) {
map { next if $_ != int $_ } map { reverse($n) / reverse $_ } divisors $n;
push @sd, $n;
}
say @sd . " matching numbers:\n" .
(sprintf "@{['%4d' x @sd]}", @sd) =~ s/(.{40})/$1\n/gr;
- Output:
72 matching numbers: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Phix
function rev(integer n) integer r = 0 while n do r = r*10+remainder(n,10) n = floor(n/10) end while return r end function function special_divisors(integer n) sequence fn = factors(n) if length(fn) then integer rn = rev(n) for i=1 to length(fn) do if remainder(rn,rev(fn[i])) then return false end if end for end if return true end function sequence res = apply(true,sprintf,{{"%3d"},filter(tagset(200),special_divisors)}) printf(1,"Found %d special divisors:\n%s\n",{length(res),join_by(res,1,18)})
- Output:
Found 72 special divisors: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
PILOT
C :max=200
:n=1
*num
C :x=n
U :*rev
C :rn=r
:d=1
*div
J (d*(n/d)<>n):*nextdiv
C :x=d
U :*rev
J (r*(rn/r)<>rn):*next
*nextdiv
C :d=d+1
J (d<=n/2):*div
T :#n
*next
C :n=n+1
J (n<max):*num
E :
*rev
C :r=0
:a=x
*revloop
C :b=a/10
:r=r+(a-b*10)
:a=b
J (a>0):*revloop
E :- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 81 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
PL/I
specialDivisors: procedure options(main);
%replace MAX by 200;
reverse: procedure(nn) returns(fixed);
declare (r, n, nn) fixed;
r = 0;
do n=nn repeat(n/10) while(n > 0);
r = r*10 + mod(n, 10);
end;
return(r);
end reverse;
isSpecial: procedure(n) returns(bit);
declare (n, rev, div) fixed;
rev = reverse(n);
do div=1 to n/2;
if mod(n, div)=0 & mod(rev, reverse(div))^=0 then
return('0'b);
end;
return('1'b);
end isSpecial;
declare (cand, col) fixed;
col = 0;
do cand=1 to MAX;
if isSpecial(cand) then do;
put edit(cand) (F(4));
col = col+1;
if mod(col, 10)=0 then put skip;
end;
end;
end specialDivisors;- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
See also #Polyglot:PL/I and PL/M
PL/M
... under CP/M (or an emulator)100H: /* FIND NUMBERS WHOSE REVERSED DIVISORS DIVIDE THE REVERSED NUMBER */
DECLARE TRUE LITERALLY '0FFH';
DECLARE FALSE LITERALLY '0';
BDOS: PROCEDURE( FN, ARG ); /* CP/M BDOS SYSTEM CALL */
DECLARE FN BYTE, ARG ADDRESS;
GOTO 5;
END BDOS;
PRINT$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PRINT$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PRINT$NL: PROCEDURE; CALL PRINT$STRING( .( 0DH, 0AH, '$' ) ); END;
PRINT$NUMBER: PROCEDURE( N );
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE;
V = N;
W = LAST( N$STR );
N$STR( W ) = '$';
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PRINT$STRING( .N$STR( W ) );
END PRINT$NUMBER;
REVERSE: PROCEDURE( N )ADDRESS; /* RETURNS THE REVERSED DIGITS OF N */
DECLARE N ADDRESS;
DECLARE ( R, V ) ADDRESS;
V = N;
R = V MOD 10;
DO WHILE( ( V := V / 10 ) > 0 );
R = ( R * 10 ) + ( V MOD 10 );
END;
RETURN R;
END REVERSE ;
/* FIND AND SHOW THE NUMBERS UP TO 200 */
DECLARE MAX$SD LITERALLY '199';
DECLARE ( N, RN, SD$COUNT, D, D$MAX ) ADDRESS;
DECLARE IS$SD BYTE;
SD$COUNT = 0;
DO N = 1 TO MAX$SD;
RN = REVERSE( N );
IS$SD = TRUE;
D = 2; D$MAX = N / 2;
DO WHILE( IS$SD AND D < D$MAX );
IF N MOD D = 0 THEN DO;
/* HAVE A DIVISOR OF N */
IS$SD = ( RN MOD REVERSE( D ) = 0 );
END;
D = D + 1;
END;
IF IS$SD THEN DO;
/* ALL THE REVERSED DIVISORS OF N DIVIDE N REVERSED */
CALL PRINT$CHAR( ' ' );
IF N < 100 THEN DO;
CALL PRINT$CHAR( ' ' );
IF N < 10 THEN CALL PRINT$CHAR( ' ' );
END;
CALL PRINT$NUMBER( N );
IF ( SD$COUNT := SD$COUNT + 1 ) MOD 10 = 0 THEN CALL PRINT$NL;
END;
END;
CALL PRINT$NL;
CALL PRINT$STRING( .'FOUND $' );
CALL PRINT$NUMBER( SD$COUNT );
CALL PRINT$STRING( .' ''''SPECIAL DIVISORS'''' BELOW $' );
CALL PRINT$NUMBER( MAX$SD + 1 );
CALL PRINT$NL;
EOF- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 FOUND 72 ''SPECIAL DIVISORS'' BELOW 200
See also #Polyglot:PL/I and PL/M
Polyglot:PL/I and PL/M
... under CP/M (or an emulator)Should work with many PL/I implementations.
The PL/I include file "pg.inc" can be found on the Polyglot:PL/I and PL/M page.
Note the use of text in column 81 onwards to hide the PL/I specifics from the PL/M compiler.
/* FIND NUMBERS WHOSE REVERSED DIVISORS DIVIDE THE REVERSED NUMBER */
special_divisors_100H: procedure options (main);
/* PL/I DEFINITIONS */
%include 'pg.inc';
/* PL/M DEFINITIONS: CP/M BDOS SYSTEM CALL AND CONSOLE I/O ROUTINES, ETC. */ /*
DECLARE BINARY LITERALLY 'ADDRESS', CHARACTER LITERALLY 'BYTE';
DECLARE SADDR LITERALLY '.', BIT LITERALLY 'BYTE';
DECLARE TRUE LITERALLY '1', FALSE LITERALLY '0';
BDOSF: PROCEDURE( FN, ARG )BYTE;
DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PRSTRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PRCHAR: PROCEDURE( C ); DECLARE C CHARACTER; CALL BDOS( 2, C ); END;
PRNL: PROCEDURE; CALL PRCHAR( 0DH ); CALL PRCHAR( 0AH ); END;
PRNUMBER: PROCEDURE( N );
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE;
N$STR( W := LAST( N$STR ) ) = '$';
N$STR( W := W - 1 ) = '0' + ( ( V := N ) MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL BDOS( 9, .N$STR( W ) );
END PRNUMBER;
MODF: PROCEDURE( A, B )ADDRESS;
DECLARE ( A, B )ADDRESS;
RETURN( A MOD B );
END MODF;
/* END LANGUAGE DEFINITIONS */
/* TASK */
REVERSE: PROCEDURE( N )returns (
BINARY )
; /* RETURNS THE REVERSED DIGITS OF N */
DECLARE N BINARY;
DECLARE ( R, V ) BINARY;
V = N;
R = MODF( V, 10 );
V = V / 10;
DO WHILE( V > 0 );
R = ( R * 10 ) + MODF( V, 10 );
V = V / 10;
END;
RETURN ( R );
END REVERSE ;
/* FIND AND SHOW THE NUMBERS UP TO 200 */
DECLARE ( N, RN, SDCOUNT, D, DMAX ) BINARY;
DECLARE ISSD BIT;
DECLARE MAXSD BINARY static INITIAL( 199 );
SDCOUNT = 0;
DO N = 1 TO MAXSD;
RN = REVERSE( N );
ISSD = TRUE;
D = 2; DMAX = N / 2;
DO WHILE( ISSD & /*
AND /* */ D < DMAX );
IF MODF( N, D ) = 0 THEN DO;
/* HAVE A DIVISOR OF N */
ISSD = ( MODF( RN, REVERSE( D ) ) = 0 );
END;
D = D + 1;
END;
IF ISSD THEN DO;
/* ALL THE REVERSED DIVISORS OF N DIVIDE N REVERSED */
CALL PRCHAR( ' ' );
IF N < 100 THEN DO;
CALL PRCHAR( ' ' );
IF N < 10 THEN CALL PRCHAR( ' ' );
END;
CALL PRNUMBER( N );
SDCOUNT = SDCOUNT + 1;
IF MODF( SDCOUNT, 10 ) = 0 THEN CALL PRNL;
END;
END;
CALL PRNL;
CALL PRSTRING( SADDR( 'FOUND $' ) );
CALL PRNUMBER( SDCOUNT );
CALL PRSTRING( SADDR( ' ''''SPECIAL DIVISORS'''' BELOW $' ) );
CALL PRNUMBER( MAXSD + 1 );
CALL PRNL;
EOF: end special_divisors_100H;- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 FOUND 72 ''SPECIAL DIVISORS'' BELOW 200
PureBasic
Procedure reverse(n.i)
u.i = 0
While n
u = u * 10 + (n % 10)
n = Int(n / 10)
Wend
ProcedureReturn u
EndProcedure
OpenConsole()
c.i = 0
For n.i = 1 To 200
u.i = reverse(n)
s.b = #True
For d.i = 1 To n
If n % d = 0
b = reverse(d)
If u % b <> 0
s = #False
EndIf
EndIf
Next d
If s
Print(Str(n) + #TAB$)
c + 1
EndIf
Next n
PrintN(#CRLF$ + "Found " + Str(c) + " special divisors.")
Input()
CloseConsole()- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23
26 27 29 31 33 37 39 41 43 44 46 47 53 55
59 61 62 66 67 69 71 73 77 79 82 83 86 88
89 93 97 99 101 103 107 109 113 121 127 131 137 139
143 149 151 157 163 167 169 173 179 181 187 191 193 197
199
Found 72 special divisors.
Python
#!/usr/bin/python
def reverse(n):
u = 0
while n:
u = 10 * u + n % 10
n = int(n / 10)
return u
c = 0
for n in range(1, 200):
u = reverse(n)
s = True
for d in range (1, n):
if n % d == 0:
b = reverse(d)
if u % b != 0:
s = False
if s:
c = c + 1
print(n, end='\t')
print("\nEncontrados ", c, "divisores especiales.")
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 Encontrados 72 divisores especiales.
Quackery
factors is defined at Factors of an integer#Quackery.
[ 0
[ swap 10 /mod
rot 10 * +
over 0 = until ]
nip ] is revnum ( n --> n )
[]
[ 200 times
[ true
i^ revnum
i^ factors
witheach
[ revnum
dip dup mod
0 != if
[ dip not
conclude ] ]
drop
if [ i^ join ] ]
behead drop ]
[]
swap witheach
[ number$ nested join ]
48 wrap$- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Raku
use Prime::Factor:ver<0.3.0+>;
say "{+$_} matching numbers:\n{.batch(10)».fmt('%3d').join: "\n"}"
given (1..^200).grep: { all .flip «%%« .&divisors».flip };
- Output:
72 matching numbers: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
REXX
/*REXX program finds special divisors: numbers N such that reverse(D) divides ··· */
/*────────────────────────── reverse(N) for all divisors D of N, where N < 200. */
parse arg hi cols . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 200 /* " " " " " " */
if cols=='' | cols=="," then cols= 10 /* " " " " " " */
w= 10 /*width of a number in any column. */
title= ' special divisors N that reverse(D) divides reverse(N) for all divisors' ,
' D of N, where N < ' hi
if cols>0 then say ' index │'center(title, 1 + cols*(w+1) )
if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─')
found= 0; idx= 1 /*initialize # found numbers and index.*/
$= /*a list of numbers found (so far). */
do j=1 for hi-1; r= reverse(j) /*search for special divisors. */
do k=2 to j%2 /*skip the first divisor (unity) & last*/
if j//k==0 then if r//reverse(k)\==0 then iterate J /*Not OK? Skip*/
end /*m*/
found= found+1 /*bump the number of special divisors. */
if cols<0 then iterate /*Build the list (to be shown later)? */
$= $ right(j, w) /*add a special divisor ──► the $ list.*/
if found//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/
if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─')
say
say 'Found ' found title
- output when using the default inputs:
index │ special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200 ───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── 1 │ 1 2 3 4 5 6 7 8 9 11 11 │ 13 17 19 22 23 26 27 29 31 33 21 │ 37 39 41 43 44 46 47 53 55 59 31 │ 61 62 66 67 69 71 73 77 79 82 41 │ 83 86 88 89 93 97 99 101 103 107 51 │ 109 113 121 127 131 137 139 143 149 151 61 │ 157 163 167 169 173 179 181 187 191 193 71 │ 197 199 ───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────── Found 72 special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200
Ring
load "stdlib.ring"
see "working..." + nl
row = 0
num = 0
limit1 = 200
for n = 1 to limit1
flag = 1
revNum = rever(string(n))
revNum = number(revNum)
for m = 1 to n/2
revDiv = rever(String(m))
revDiv = number(revDiv)
if n%m = 0
if revNum % revDiv = 0
flag = 1
else
flag = 0
exit
ok
ok
next
if flag = 1
num = num + 1
row = row + 1
see "" + n + " "
if row%10 = 0
see nl
ok
ok
next
see nl + "Found " + num + " special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200" + nl
see "done..." + nl
func rever(str)
rev = ""
for n = len(str) to 1 step -1
rev = rev + str[n]
next
return rev- Output:
working... 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 Found 72 special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200 done...
RPL
≪ →STR ""
OVER SIZE 1 FOR j
OVER j DUP SUB +
-1 STEP
STR→ NIP
≫ 'REVNUM' STO
≪ {1}
2 200 FOR n
1 SF
n REVNUM n DIVIS
2 OVER SIZE 1 - FOR d
IF DUP2 d GET REVNUM MOD THEN
1 CF DUP SIZE 'd' STO END
NEXT DROP2
IF 1 FS? THEN n + END
NEXT
≫ 'TASK' STO
- Output:
1: {1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199}
Runs in 62 seconds on a HP-50g.
Ruby
class Integer
def reverse
to_s.reverse.to_i
end
def divisors
res = []
(1..Integer.sqrt(self)).each do |cand|
div, mod = self.divmod(cand)
res << cand << div if mod == 0
end
res.uniq.sort
end
def special_divisors?
r = self.reverse
divisors.all?{|d| r % d.reverse == 0}
end
end
p (1..200).select(&:special_divisors?)
- Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 19, 22, 23, 26, 27, 29, 31, 33, 37, 39, 41, 43, 44, 46, 47, 53, 55, 59, 61, 62, 66, 67, 69, 71, 73, 77, 79, 82, 83, 86, 88, 89, 93, 97, 99, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199]
Sidef
1..200 -> grep {|n| n.divisors.all {|d| d.flip `divides` n.flip } }.say
- Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 19, 22, 23, 26, 27, 29, 31, 33, 37, 39, 41, 43, 44, 46, 47, 53, 55, 59, 61, 62, 66, 67, 69, 71, 73, 77, 79, 82, 83, 86, 88, 89, 93, 97, 99, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199]
Swift
import Foundation
func reverse(_ number: Int) -> Int {
var rev = 0
var n = number
while n > 0 {
rev = rev * 10 + n % 10
n /= 10
}
return rev
}
func special(_ number: Int) -> Bool {
var n = 2
let rev = reverse(number)
while n * n <= number {
if number % n == 0 {
if rev % reverse(n) != 0 {
return false
}
let m = number / n
if m != n && rev % reverse(m) != 0 {
return false
}
}
n += 1
}
return true
}
var count = 0
for n in 1..<200 {
if special(n) {
count += 1
print(String(format: "%3d", n),
terminator: count % 10 == 0 ? "\n" : " ")
}
}
print("\n\(count) numbers found.")
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 72 numbers found.
Wren
import "/math" for Int
import "/seq" for Lst
import "/fmt" for Fmt
var reversed = Fn.new { |n|
var rev = 0
while (n > 0) {
rev = rev * 10 + n % 10
n = (n/10).floor
}
return rev
}
var special = []
for (n in 1...200) {
var divs = Int.divisors(n)
var revN = reversed.call(n)
if (divs.all { |d| revN % reversed.call(d) == 0 }) special.add(n)
}
System.print("Special divisors in the range 0..199:")
for (chunk in Lst.chunks(special, 12)) Fmt.print("$3d", chunk)
System.print("\n%(special.count) special divisors found.")- Output:
Special divisors in the range 0..199: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 72 special divisors found.
XPL0
func Reverse(N); \Reverse the order of the digits
int N, M;
[M:= 0;
repeat N:= N/10;
M:= M*10 + rem(0);
until N = 0;
return M;
];
func Test(N);
\Return 'true' if reverse(D) divides reverse(N) for all divisors D of N
int N, D, RevNum, RevDiv;
[RevNum:= Reverse(N);
for D:= 1 to N/2 do
if rem(N/D) = 0 then
[RevDiv:= Reverse(D);
if rem(RevNum/RevDiv) then return false;
];
return true;
];
int Count, N;
[Count:= 0;
for N:= 1 to 199 do
[if Test(N) then
[IntOut(0, N);
Count:= Count+1;
if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);
];
];
CrLf(0);
IntOut(0, Count);
Text(0, " such numbers found.");
]- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 72 such numbers found.
Yabasic
// Rosetta Code problem: http://rosettacode.org/wiki/Special_divisors
// by Galileo, 04/2022
20 FOR I=1 TO 199
30 J=I: X=0
40 IF J>0 X=X*10+MOD(J, 10): J=INT(J/10): GOTO 40
50 FOR J=1 TO INT(I/2)
60 IF MOD(I, J) GOTO 100
70 K=J: Y=0
80 IF K>0 Y=Y*10+MOD(K, 10): K=INT(K/10): GOTO 80
90 IF MOD(X, Y) GOTO 120
100 NEXT J
110 PRINT I,
120 NEXT I- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 ---Program done, press RETURN---
Zig
const MAX = 200; // max number to check
const N = u16; // smallest integer type that fits
pub fn reverse(n: N) N {
var r: N = 0;
var nn = n;
while (nn > 0) : (nn /= 10)
r = r*10 + nn%10;
return r;
}
pub fn special(n: N) bool {
var r = reverse(n);
var d: N = 1;
while (d <= n/2) : (d += 1)
if (n % d == 0 and r % reverse(d) != 0)
return false;
return true;
}
pub fn main() !void {
const stdout = @import("std").io.getStdOut().writer();
var c: N = 0;
var n: N = 1;
while (n <= MAX) : (n += 1) {
if (special(n)) {
try stdout.print("{d:4}", .{n});
c += 1;
if (c % 10 == 0) try stdout.print("\n", .{});
}
}
try stdout.print("\n", .{});
}
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
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