Special divisors

Numbers   n   such that   reverse(d)   divides   reverse(n)   for all divisors   d   of   n,   where   n  <  200

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.

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:
```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

Translation of: ALGOL 68
```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

Works with: Dyalog 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

Translation of: Delphi
```#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#

Translation of: 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

Translation of: Ring
```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;
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...```

EasyLang

Translation of: Python
```func reverse s .
while s > 0
e = e * 10 + s mod 10
s = s div 10
.
return e
.
for n = 1 to 199
u = reverse n
for d = 1 to n - 1
if n mod d = 0
b = reverse d
if u mod b <> 0
break 1
.
.
.
if d = n
write 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
```

Factor

Works with: Factor version 0.99 2021-02-05
```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

Works with: Gforth
```: 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 n
```

Go

Translation of: Wren
Library: Go-rcu
```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: 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:

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
```

```            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:
if d * d != n:
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```

Perl

Library: ntheory
```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```

PL/M

Works with: 8080 PL/M Compiler

... 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 */
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 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 ( 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
```

Polyglot:PL/I and PL/M

Works with: 8080 PL/M Compiler

... 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 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;
RETURN( A MOD B );
END MODF;
/* END LANGUAGE DEFINITIONS */

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')

```
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

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 ] ]
[]
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

Works with: HP version 49
```≪ →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
```
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]
```

Rust

```fn condition( num : u16 ) -> bool {
let divis : Vec<u16> = divisors( num ) ;
let reversed : u16 = my_reverse( num ) ;
divis.iter( ).all( | d | {
let revi = my_reverse( *d ) ;
reversed % revi == 0 } )
}

fn my_reverse( num : u16 ) -> u16 {
let numstring : String = num.to_string( ) ;
let nstr : &str = numstring.as_str( ) ;
let mut reversed_str : String = String::new( ) ;
for c in  nstr.chars( ).rev( ) {
reversed_str.push( c ) ;
}
let reversi : &str = reversed_str.as_str( ) ;
reversi.parse::<u16>( ).unwrap( )
}

fn divisors( n : u16 ) -> Vec<u16> {
(1..=n).filter( | &d | n % d == 0 ).collect( )
}

fn main() {
println!("{:?}" , (1u16..200u16).filter( | &d | condition( d ) ).collect
::<Vec<u16>>( ) )  ;
}
```
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

Library: Wren-math
Library: Wren-fmt
```import "./math" for Int
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:")
Fmt.tprint("\$3d", special, 12)
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

Translation of: BASIC
```// 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```