Factorions

Definition

A factorion is a natural number that equals the sum of the factorials of its digits.

Example

145 is a factorion in base 10 because:

1! + 4! + 5! = 1 + 24 + 120 = 145

It can be shown (see the Wikipedia article below) that no factorion in base 10 can exceed 1,499,999.

Task

Write a program in your language to demonstrate, by calculating and printing out the factorions, that:

There are 3 factorions in base 9
There are 4 factorions in base 10
There are 5 factorions in base 11
There are 2 factorions in base 12 (up to the same upper bound as for base 10)

See also

Wikipedia article
OEIS:A014080 - Factorions in base 10
OEIS:A193163 - Factorions in base n

360 Assembly[edit]

*        Factorions                26/04/2020
FACTORIO CSECT
         USING  FACTORIO,R13       base register
         B      72(R15)            skip savearea
         DC     17F'0'             savearea
         SAVE   (14,12)            save previous context
         ST     R13,4(R15)         link backward
         ST     R15,8(R13)         link forward
         LR     R13,R15            set addressability
         XR     R4,R4              ~
         LA     R5,1               f=1
         LA     R3,FACT+4          @fact(1)
         LA     R6,1               i=1
       DO WHILE=(C,R6,LE,=A(NN2))  do i=1 to nn2
         MR     R4,R6                fact(i-1)*i
         ST     R5,0(R3)             fact(i)=fact(i-1)*i
         LA     R3,4(R3)             @fact(i+1)
         LA     R6,1(R6)             i++
       ENDDO    ,                  enddo i
         LA     R7,NN1             base=nn1
       DO WHILE=(C,R7,LE,=A(NN2))  do base=nn1 to nn2
	     MVC    PG,PGX               init buffer
         LA     R3,PG+6              @buffer
         XDECO  R7,XDEC              edit base
         MVC    PG+5(2),XDEC+10      output base
         LA     R3,PG+10             @buffer
         LA     R6,1                 i=1
       DO WHILE=(C,R6,LE,LIM)        do i=1 to lim 
         LA     R9,0                   s=0
         LR     R8,R6                  t=i
       DO WHILE=(C,R8,NE,=F'0')        while t<>0
         XR     R4,R4                    ~
         LR     R5,R8                    t 
         DR     R4,R7                    r5=t/base; r4=d=(t mod base)
         LR     R1,R4                    d
         SLA    R1,2                     ~
         L      R2,FACT(R1)              fact(d)
         AR     R9,R2                    s=s+fact(d)
         LR     R8,R5                    t=t/base
       ENDDO    ,                      endwhile
       IF    CR,R9,EQ,R6 THEN          if s=i then
         XDECO  R6,XDEC                  edit i
         MVC    0(6,R3),XDEC+6           output i
         LA     R3,7(R3)                 @buffer
       ENDIF    ,                      endif
         LA     R6,1(R6)               i++
       ENDDO    ,                    enddo i
         XPRNT  PG,L'PG              print buffer
         LA     R7,1(R7)             base++
       ENDDO    ,                  enddo base
         L      R13,4(0,R13)       restore previous savearea pointer
         RETURN (14,12),RC=0       restore registers from calling save
NN1      EQU    9                  nn1=9
NN2      EQU    12                 nn2=12
LIM      DC     f'1499999'         lim=1499999
FACT     DC     (NN2+1)F'1'        fact(0:12)
PG       DS     CL80               buffer
PGX      DC     CL80'Base .. : '   buffer init
XDEC     DS     CL12               temp fo xdeco
         REGEQU
         END    FACTORIO

Output:

Base  9 :      1      2  41282
Base 10 :      1      2    145  40585
Base 11 :      1      2     26     48  40472
Base 12 :      1      2

ALGOL 68[edit]

Translation of: C

BEGIN
    # cache factorials from 0 to 11 #
    [ 0 : 11 ]INT fact;
    fact[0] := 1;
    FOR n TO 11 DO
        fact[n] := fact[n-1] * n
    OD;
    FOR b FROM 9 TO 12 DO
        print( ( "The factorions for base ", whole( b, 0 ), " are:", newline ) );
        FOR i TO 1500000 - 1 DO
            INT sum := 0;
            INT j := i;
            WHILE j > 0 DO
                sum +:= fact[ j MOD b ];
                j OVERAB b
            OD;
            IF sum = i THEN print( ( whole( i, 0 ), " " ) ) FI
        OD;
        print( ( newline ) )
    OD
END

Output:

The factorions for base 9 are:
1 2 41282
The factorions for base 10 are:
1 2 145 40585
The factorions for base 11 are:
1 2 26 48 40472
The factorions for base 12 are:
1 2

Applesoft BASIC[edit]

100 DIM FACT(12)
110 FACT(0) = 1
120 FOR N = 1 TO 11
130     FACT(N) = FACT(N - 1) * N
140 NEXT 
200 FOR B = 9 TO 12
210     PRINT "THE FACTORIONS ";
215     PRINT "FOR BASE "B" ARE:"
220     FOR I = 1 TO 1499999
230         SUM = 0
240         FOR J = I TO 0 STEP 0
245             M =  INT (J / B)
250             D = J - M * B
260             SUM = SUM + FACT(D)
270             J = M
280         NEXT J
290         IF SU = I THEN  PRINT I" ";
300     NEXT I
310     PRINT : PRINT 
320 NEXT B

AutoHotkey[edit]

Translation of: C

fact:=[]
fact[0] := 1
while (A_Index < 12)
	fact[A_Index] := fact[A_Index-1] * A_Index
b := 9
while (b <= 12) {
	res .= "base " b " factorions:  `t"
	while (A_Index < 1500000){
		sum := 0
		j := A_Index
		while (j > 0){
			d := Mod(j, b)
			sum += fact[d]
			j /= b
		}
		if (sum = A_Index) 
			res .= A_Index "  "
	}
	b++
	res .= "`n"
}
MsgBox % res
return

Output:

base 9 factorions:  	1  2  41282  
base 10 factorions:  	1  2  145  40585  
base 11 factorions:  	1  2  26  48  40472  
base 12 factorions:  	1  2

AWK[edit]

 
# syntax: GAWK -f FACTORIONS.AWK
# converted from C
BEGIN {
    fact[0] = 1 # cache factorials from 0 to 11
    for (n=1; n<12; ++n) {
      fact[n] = fact[n-1] * n
    }
    for (b=9; b<=12; ++b) {
      printf("base %d factorions:",b)
      for (i=1; i<1500000; ++i) {
        sum = 0
        j = i
        while (j > 0) {
          d = j % b
          sum += fact[d]
          j = int(j/b)
        }
        if (sum == i) {
          printf(" %d",i)
        }
      }
      printf("\n")
    }
    exit(0)
}

Output:

base 9 factorions: 1 2 41282
base 10 factorions: 1 2 145 40585
base 11 factorions: 1 2 26 48 40472
base 12 factorions: 1 2

C[edit]

Translation of: Go

#include <stdio.h>
 
int main() {    
    int n, b, d;
    unsigned long long i, j, sum, fact[12];
    // cache factorials from 0 to 11
    fact[0] = 1;
    for (n = 1; n < 12; ++n) {
        fact[n] = fact[n-1] * n;
    }
 
    for (b = 9; b <= 12; ++b) {
        printf("The factorions for base %d are:\n", b);
        for (i = 1; i < 1500000; ++i) {
            sum = 0;
            j = i;
            while (j > 0) {
                d = j % b;
                sum += fact[d];
                j /= b;
            }
            if (sum == i) printf("%llu ", i);
        }
        printf("\n\n");
    }
    return 0;
}

Output:

The factorions for base 9 are:
1 2 41282 

The factorions for base 10 are:
1 2 145 40585 

The factorions for base 11 are:
1 2 26 48 40472 

The factorions for base 12 are:
1 2

C++[edit]

Translation of: C

#include <iostream>
 
class factorion_t {
public:
    factorion_t() {
        f[0] = 1u;
        for (uint n = 1u; n < 12u; n++)
            f[n] = f[n - 1] * n;
    }
 
    bool operator()(uint i, uint b) const {
        uint sum = 0;
        for (uint j = i; j > 0u; j /= b)
            sum += f[j % b];
        return sum == i;
    }
 
private:
    ulong f[12];  //< cache factorials from 0 to 11
};
 
int main() {
    factorion_t factorion;
    for (uint b = 9u; b <= 12u; ++b) {
        std::cout << "factorions for base " << b << ':';
        for (uint i = 1u; i < 1500000u; ++i)
            if (factorion(i, b))
                std::cout << ' ' << i;
        std::cout << std::endl;
    }
    return 0;
}

Output:

factorions for base 9: 1 2 41282
factorions for base 10: 1 2 145 40585
factorions for base 11: 1 2 26 48 40472
factorions for base 12: 1 2

Delphi[edit]

Library: System.SysUtils

Translation of: C

 
program Factorions;
 
{$APPTYPE CONSOLE}
 
uses
  System.SysUtils;
 
begin
  var fact: TArray<UInt64>;
  SetLength(fact, 12);
 
  fact[0] := 0;
  for var n := 1 to 11 do
    fact[n] := fact[n - 1] * n;
 
  for var b := 9 to 12 do
  begin
    writeln('The factorions for base ', b, ' are:');
    for var i := 1 to 1499999 do
    begin
      var sum := 0;
      var j := i;
      while j > 0 do
      begin
        var d := j mod b;
        sum := sum + fact[d];
        j := j div b;
      end;
      if sum = i then
        writeln(i, ' ');
    end;
    writeln(#10);
  end;
  readln;
end.

Factor[edit]

USING: formatting io kernel math math.parser math.ranges memoize
prettyprint sequences ;
IN: rosetta-code.factorions
 
! Memoize factorial function
MEMO: factorial ( n -- n! ) [ 1 ] [ [1,b] product ] if-zero ;
 
: factorion? ( n base -- ? )
    dupd >base string>digits [ factorial ] map-sum = ;
 
: show-factorions ( limit base -- )
    dup "The factorions for base %d are:\n" printf
    [ [1,b) ] dip [ dupd factorion? [ pprint bl ] [ drop ] if ]
    curry each nl ;
 
1,500,000 9 12 [a,b] [ show-factorions nl ] with each

Output:

The factorions for base 9 are:
1 2 41282 

The factorions for base 10 are:
1 2 145 40585 

The factorions for base 11 are:
1 2 26 48 40472 

The factorions for base 12 are:
1 2

Fōrmulæ[edit]

In this page you can see the solution of this task.

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). 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 transportation effects more than visualization and edition.

The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.

FreeBASIC[edit]

Dim As Integer fact(12), suma, d, j
fact(0) = 1
For n As Integer = 1 To 11
    fact(n) = fact(n-1) * n
Next n
For b As Integer = 9 To 12
    Print "Los factoriones para base " & b & " son: "
    For i As Integer = 1 To 1499999
        suma = 0
        j = i
        While j > 0
            d = j Mod b
            suma += fact(d)
            j \= b
        Wend
        If suma = i Then Print i & " ";
    Next i
    Print : Print
Next b
Sleep

Output:

Los factoriones para base 9 son:
1 2 41282

Los factoriones para base 10 son:
1 2 145 40585

Los factoriones para base 11 son:
1 2 26 48 40472

Los factoriones para base 12 son:
1 2

Frink[edit]

factorion[n, base] := sum[map["factorial", integerDigits[n, base]]]
 
for base = 9 to 12
{
   for n = 1 to 1_499_999
      if n == factorion[n, base]
         println["$base\t$n"]
}

Output:

Go[edit]

package main
 
import (
    "fmt"
    "strconv"
)
 
func main() {
    // cache factorials from 0 to 11
    var fact [12]uint64
    fact[0] = 1
    for n := uint64(1); n < 12; n++ {
        fact[n] = fact[n-1] * n
    }
 
    for b := 9; b <= 12; b++ {
        fmt.Printf("The factorions for base %d are:\n", b)
        for i := uint64(1); i < 1500000; i++ {
            digits := strconv.FormatUint(i, b)
            sum := uint64(0)
            for _, digit := range digits {
                if digit < 'a' {
                    sum += fact[digit-'0']
                } else {
                    sum += fact[digit+10-'a']
                }
            }
            if sum == i {
                fmt.Printf("%d ", i)
            }
        }
        fmt.Println("\n")
    }
}

Output:

The factorions for base 9 are:
1 2 41282 

The factorions for base 10 are:
1 2 145 40585 

The factorions for base 11 are:
1 2 26 48 40472 

The factorions for base 12 are:
1 2

Haskell[edit]

import Text.Printf (printf)
import Data.List (unfoldr)
import Control.Monad (guard)
 
factorion :: Int -> Int -> Bool
factorion b n = f b n == n
 where
  f b = sum . map (product . enumFromTo 1) . unfoldr (\x -> guard (x > 0) >> pure (x `mod` b, x `div` b))
 
main :: IO ()
main = mapM_ (uncurry (printf "Factorions for base %2d: %s\n") . (\(a, b) -> (b, result a b))) 
  [(3,9), (4,10), (5,11), (2,12)]
 where 
  factorions b = filter (factorion b) [1..]
  result n = show . take n . factorions

Output:

Factorions for base  9: [1,2,41282]
Factorions for base 10: [1,2,145,40585]
Factorions for base 11: [1,2,26,48,40472]
Factorions for base 12: [1,2]

J[edit]

 
   index=: $ #: [email protected]:,
   factorion=: 10&$: :(] = [: +/ [: ! #.^:_1)&>
 
   FACTORIONS=: 9 0 +"1 index Q=: 9 10 11 12 factorion/ i. 1500000
 
   NB. base, factorion expressed in bases 10, and base
   (,. "[email protected]:((Num_j_,26}.Alpha_j_) {~ #.inv/)"1) FACTORIONS
 9     1     1
 9     2     2
 9 41282 62558
10     1     1
10     2     2
10   145   145
10 40585 40585
11     1     1
11     2     2
11    26    24
11    48    44
11 40472 28453
12     1     1
12     2     2
 
   NB. tallies of factorions in the bases
   (9+i.4),.+/"1 Q
 9 3
10 4
11 5
12 2

Java[edit]

 
public class Factorion {
    public static void main(String [] args){
        System.out.println("Base 9:");
        for(int i = 1; i <= 1499999; i++){
            String iStri = String.valueOf(i);
            int multiplied = operate(iStri,9);
            if(multiplied == i){
                System.out.print(i + "\t");
            }
        }
        System.out.println("\nBase 10:");
        for(int i = 1; i <= 1499999; i++){
            String iStri = String.valueOf(i);
            int multiplied = operate(iStri,10);
            if(multiplied == i){
                System.out.print(i + "\t");
            }
        }
        System.out.println("\nBase 11:");
        for(int i = 1; i <= 1499999; i++){
            String iStri = String.valueOf(i);
            int multiplied = operate(iStri,11);
            if(multiplied == i){
                System.out.print(i + "\t");
            }
        }
        System.out.println("\nBase 12:");
        for(int i = 1; i <= 1499999; i++){
            String iStri = String.valueOf(i);
            int multiplied = operate(iStri,12);
            if(multiplied == i){
                System.out.print(i + "\t");
            }
        }
    }
    public static int factorialRec(int n){
        int result = 1;
        return n == 0 ? result : result * n * factorialRec(n-1);
    }
 
    public static int operate(String s, int base){
        int sum = 0;
        String strx = fromDeci(base, Integer.parseInt(s));
        for(int i = 0; i < strx.length(); i++){
            if(strx.charAt(i) == 'A'){
                sum += factorialRec(10);
            }else if(strx.charAt(i) == 'B') {
                sum += factorialRec(11);
            }else if(strx.charAt(i) == 'C') {
                sum += factorialRec(12);
            }else {
                sum += factorialRec(Integer.parseInt(String.valueOf(strx.charAt(i)), base));
            }
        }
        return sum;
    }
    // Ln 57-71 from Geeks for Geeks @ https://www.geeksforgeeks.org/convert-base-decimal-vice-versa/
    static char reVal(int num) {
        if (num >= 0 && num <= 9)
            return (char)(num + 48);
        else
            return (char)(num - 10 + 65);
    }
    static String fromDeci(int base, int num){
        StringBuilder s = new StringBuilder();
        while (num > 0) {
            s.append(reVal(num % base));
            num /= base;
        }
        return new String(new StringBuilder(s).reverse());
    }
}

Output:

Base 9:
1	2	41282	
Base 10:
1	2	145	40585	
Base 11:
1	2	26	48	40472	
Base 12:
1	2

Julia[edit]

isfactorian(n, base) = mapreduce(factorial, +, map(c -> parse(Int, c, base=16), split(string(n, base=base), ""))) == n
 
printallfactorian(base) = println("Factorians for base $base: ", [n for n in 1:100000 if isfactorian(n, base)])
 
foreach(printallfactorian, 9:12)

Output:

Factorians for base 9: [1, 2, 41282]
Factorians for base 10: [1, 2, 145, 40585]
Factorians for base 11: [1, 2, 26, 48, 40472]
Factorians for base 12: [1, 2]

Nim[edit]

Note that the library has precomputed the values of factorial, so there is no need for caching.

from math import fac
from strutils import join
 
iterator digits(n, base: Natural): Natural =
  ## Yield the digits of "n" in base "base".
  var n = n
  while true:
    yield n mod base
    n = n div base
    if n == 0: break
 
func isFactorion(n, base: Natural): bool =
  ## Return true if "n" is a factorion for base "base".
  var s = 0
  for d in n.digits(base):
    inc s, fac(d)
  result = s == n
 
func factorions(base, limit: Natural): seq[Natural] =
  ## Return the list of factorions for base "base" up to "limit".
  for n in 1..limit:
    if n.isFactorion(base):
      result.add(n)
 
 
for base in 9..12:
  echo "Factorions for base ", base, ':'
  echo factorions(base, 1_500_000 - 1).join(" ")

Output:

Factorions for base 9:
1 2 41282
Factorions for base 10:
1 2 145 40585
Factorions for base 11:
1 2 26 48 40472
Factorions for base 12:
1 2

OCaml[edit]

Translation of: C

let () =
  (* cache factorials from 0 to 11 *)
  let fact = Array.make 12 0 in
  fact.(0) <- 1;
  for n = 1 to pred 12 do
    fact.(n) <- fact.(n-1) * n;
  done;
 
  for b = 9 to 12 do
    Printf.printf "The factorions for base %d are:\n" b;
    for i = 1 to pred 1_500_000 do
      let sum = ref 0 in
      let j = ref i in
      while !j > 0 do
        let d = !j mod b in
        sum := !sum + fact.(d);
        j := !j / b;
      done;
      if !sum = i then (print_int i; print_string " ")
    done;
    print_string "\n\n";
  done

Perl[edit]

Translation of: Raku

Library: ntheory

use strict;
use warnings;
use ntheory qw/factorial todigits/;
 
my $limit = 1500000;
 
for my $b (9 .. 12) {
    print "Factorions in base $b:\n";
    $_ == factorial($_) and print "$_ " for 0..$b-1;
 
    for my $i (1 .. int $limit/$b) {
        my $sum;
        my $prod = $i * $b;
 
        for (reverse todigits($i, $b)) {
            $sum += factorial($_);
            $sum = 0 && last if $sum > $prod;
        }
 
        next if $sum == 0;
        ($sum + factorial($_) == $prod + $_) and print $prod+$_ . ' ' for 0..$b-1;
    }
    print "\n\n";
}

Output:

Factorions in base 9:
1 2 41282

Factorions in base 10:
1 2 145 40585

Factorions in base 11:
1 2 26 48 40472

Factorions in base 12:
1 2

Alternatively, a more efficient approach:

Translation of: Sidef

Library: ntheory

use 5.020;
use ntheory qw(:all);
use experimental qw(signatures);
use Algorithm::Combinatorics qw(combinations_with_repetition);
 
sub max_power ($base = 10) {
    my $m = 1;
    my $f = factorial($base - 1);
    while ($m * $f >= $base**($m-1)) {
        $m += 1;
    }
    return $m-1;
}
 
sub factorions ($base = 10) {
 
    my @result;
    my @digits    = (0 .. $base-1);
    my @factorial = map { factorial($_) } @digits;
 
    foreach my $k (1 .. max_power($base)) {
        my $iter = combinations_with_repetition(\@digits, $k);
        while (my $comb = $iter->next) {
            my $n = vecsum(map { $factorial[$_] } @$comb);
            if (join(' ', sort { $a <=> $b } todigits($n, $base)) eq join(' ', @$comb)) {
                push @result, $n;
            }
        }
    }
 
    return @result;
}
 
foreach my $base (2 .. 14) {
    my @r = factorions($base);
    say "Factorions in base $base are (@r)";
}

Output:

Factorions in base 2 are (1 2)
Factorions in base 3 are (1 2)
Factorions in base 4 are (1 2 7)
Factorions in base 5 are (1 2 49)
Factorions in base 6 are (1 2 25 26)
Factorions in base 7 are (1 2)
Factorions in base 8 are (1 2)
Factorions in base 9 are (1 2 41282)
Factorions in base 10 are (1 2 145 40585)
Factorions in base 11 are (1 2 26 48 40472)
Factorions in base 12 are (1 2)
Factorions in base 13 are (1 2 519326767)
Factorions in base 14 are (1 2 12973363226)

Phix[edit]

Translation of: C

-- cache factorials from 0 to 11
sequence fact = repeat(1,12)
for n=2 to length(fact) do
    fact[n] = fact[n-1]*(n-1)
end for
 
for b=9 to 12 do
    printf(1,"The factorions for base %d are:\n", b)
    for i=1 to 1499999 do
        atom total = 0, j = i, d
        while j>0 and total<=i do
            d = remainder(j,b)
            total += fact[d+1]
            j = floor(j/b)
        end while
        if total==i then printf(1,"%d ", i) end if
    end for
    printf(1,"\n\n")
end for

Output:

The factorions for base 9 are:
1 2 41282

The factorions for base 10 are:
1 2 145 40585

The factorions for base 11 are:
1 2 26 48 40472

The factorions for base 12 are:
1 2

Python[edit]

Translation of: C

fact = [1] # cache factorials from 0 to 11
for n in range(1, 12):
    fact.append(fact[n-1] * n)
 
for b in range(9, 12+1):
    print(f"The factorions for base {b} are:")
    for i in range(1500000):
        fact_sum = 0
        j = i
        while j > 0:
            d = j % b
            fact_sum += fact[d]
            j = j//b
        if fact_sum == i:
            print(i, end=" ")
    print()

Output:

The factorions for base 9 are:
1 2 41282

The factorions for base 10 are:
1 2 145 40585

The factorions for base 11 are:
1 2 26 48 40472

The factorions for base 12 are:
1 2

Racket[edit]

Translation of: C

#lang racket
 
(define fact
  (curry list-ref (for/fold ([result (list 1)] #:result (reverse result))
                            ([x (in-range 1 20)])
                    (cons (* x (first result)) result))))
 
(for ([b (in-range 9 13)])
  (printf "The factorions for base ~a are:\n" b)
  (for ([i (in-range 1 1500000)])
    (let loop ([sum 0] [n i])
      (cond
        [(positive? n) (loop (+ sum (fact (modulo n b))) (quotient n b))]
        [(= sum i) (printf "~a " i)])))
  (newline))

Output:

The factorions for base 9 are:
1 2 41282 
The factorions for base 10 are:
1 2 145 40585 
The factorions for base 11 are:
1 2 26 48 40472 
The factorions for base 12 are:
1 2

Raku[edit]

(formerly Perl 6)

Works with: Rakudo version 2019.07.1

constant @factorial = 1, |[\*] 1..*;
 
constant $limit = 1500000;
 
constant $bases = 9 .. 12;
 
my @result;
 
$bases.race(:1batch).map: -> $base {
 
    @result[$base] = "\nFactorions in base $base:\n1 2";
 
    sink (1 .. $limit div $base).map: -> $i {
        my $product = $i * $base;
        my $partial;
 
        for $i.polymod($base xx *) {
            $partial += @factorial[$_];
            last if $partial > $product
        }
 
        next if $partial > $product;
 
        my $sum;
 
        for ^$base {
            last if ($sum = $partial + @factorial[$_]) > $product + $_;
            @result[$base] ~= " $sum" and last if $sum == $product + $_
        }
    }
}
 
.say for @result[$bases];

Output:

Factorions in base 9:
1 2 41282

Factorions in base 10:
1 2 145 40585

Factorions in base 11:
1 2 26 48 40472

Factorions in base 12:
1 2

REXX[edit]

Translation of: C

/*REXX program calculates and displays   factorions   in  bases  nine ───► twelve.      */
parse arg LOb HIb lim .                          /*obtain optional arguments from the CL*/
if LOb=='' | LOb==","  then LOb=       9         /*Not specified?  Then use the default.*/
if HIb=='' | HIb==","  then HIb=      12         /* "      "         "   "   "      "   */
if lim=='' | lim==","  then lim= 1500000  -  1   /* "      "         "   "   "      "   */
 
  do fact=0  to HIb;   !.fact= !(fact)           /*use memoization for factorials.      */
  end   /*fact*/
 
  do base=LOb  to  HIb                           /*process all the required bases.      */
  @= 1 2                                         /*initialize the list  (@)  to  1 & 2. */
          do j=3  for lim-2;  $= 0               /*initialize the sum   ($)  to  zero.  */
                                          t= j   /*define the target  (for the sum !'s).*/
                                 do until t==0;    d= t // base      /*obtain a "digit".*/
                                                   $= $ + !.d        /*add  !(d) to sum.*/
                                                   t= t % base       /*get a new target.*/
                                 end   /*until*/
          if $==j  then @= @ j                   /*Good factorial sum? Then add to list.*/
          end   /*i*/
  say
  say 'The factorions for base '      right( base, length(HIb) )        " are: "         @
  end   /*base*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
!: procedure; parse arg x;  !=1;    do j=2  to x;  !=!*j;  end;   return !  /*factorials*/

output when using the default inputs:

The factorions for base   9  are:  1 2 41282

The factorions for base  10  are:  1 2 145 40585

The factorions for base  11  are:  1 2 26 48 40472

The factorions for base  12  are:  1 2

Ring[edit]

 
load "stdlib.ring"
 
for n = 1 to 100000
    fac = 0
    numStr = string(n)
    for m = 1 to len(numStr)
        num = number(numStr[m])
        fac = fac + factorial(num)
    next
    if n = fac  
       see "Factorion: " + n + nl
    ok
next

Factorion: 1
Factorion: 2
Factorion: 145
Factorion: 40585

Ruby[edit]

 
def factorion?(n, base)
  n.digits(base).sum{|digit| (1..digit).inject(1, :*)} == n 
end
 
(9..12).each do |base|
  puts "Base #{base} factorions: #{(1..1_500_000).select{|n| factorion?(n, base)}.join(" ")} "
end

Output:

Base 9 factorions: 1 2 41282 
Base 10 factorions: 1 2 145 40585 
Base 11 factorions: 1 2 26 48 40472 
Base 12 factorions: 1 2

Scala[edit]

Translation of: C++

object Factorion extends App {
    private def is_factorion(i: Int, b: Int): Boolean = {
        var sum = 0L
        var j = i
        while (j > 0) {
            sum +=  f(j % b)
            j /= b
        }
        sum == i
    }
 
    private val f = Array.ofDim[Long](12)
    f(0) = 1L
    (1 until 12).foreach(n => f(n) = f(n - 1) * n)
    (9 to 12).foreach(b => {
        print(s"factorions for base $b:")
        (1 to 1500000).filter(is_factorion(_, b)).foreach(i => print(s" $i"))
        println
    })
}

Sidef[edit]

func max_power(b = 10) {
    var m = 1
    var f = (b-1)!
    while (m*f >= b**(m-1)) {
        m += 1
    }
    return m-1
}
 
func factorions(b = 10) {
 
    var result = []
    var digits = @^b
    var fact = digits.map { _! }
 
    for k in (1 .. max_power(b)) {
        digits.combinations_with_repetition(k, {|*comb|
            var n = comb.sum_by { fact[_] }
            if (n.digits(b).sort == comb) {
                result << n
            }
        })
    }
 
    return result
}
 
for b in (2..12) {
    var r = factorions(b)
    say "Base #{'%2d' % b} factorions: #{r}"
}

Output:

Base  2 factorions: [1, 2]
Base  3 factorions: [1, 2]
Base  4 factorions: [1, 2, 7]
Base  5 factorions: [1, 2, 49]
Base  6 factorions: [1, 2, 25, 26]
Base  7 factorions: [1, 2]
Base  8 factorions: [1, 2]
Base  9 factorions: [1, 2, 41282]
Base 10 factorions: [1, 2, 145, 40585]
Base 11 factorions: [1, 2, 26, 48, 40472]
Base 12 factorions: [1, 2]

Swift[edit]

Translation of: C

var fact = Array(repeating: 0, count: 12)
 
fact[0] = 1
 
for n in 1..<12 {
  fact[n] = fact[n - 1] * n
}
 
for b in 9...12 {
  print("The factorions for base \(b) are:")
 
  for i in 1..<1500000 {
    var sum = 0
    var j = i
 
    while j > 0 {
      sum += fact[j % b]
      j /= b
    }
 
    if sum == i {
      print("\(i)", terminator: " ")
      fflush(stdout)
    }
  }
 
  print("\n")
}

Output:

The factorions for base 9 are:
1 2 41282 

The factorions for base 10 are:
1 2 145 40585 

The factorions for base 11 are:
1 2 26 48 40472 

The factorions for base 12 are:
1 2

Wren[edit]

Translation of: C

// cache factorials from 0 to 11
var fact = List.filled(12, 0)
fact[0] = 1
for (n in 1..11) fact[n] = fact[n-1] * n
 
for (b in 9..12) {
    System.print("The factorions for base %(b) are:")
    for (i in 1...1500000) {
        var sum = 0
        var j = i
        while (j > 0) {
            var d = j % b
            sum = sum + fact[d]
            j = (j/b).floor
        }
        if (sum == i) System.write("%(i) ")
    }
    System.print("\n")
}

Output:

The factorions for base 9 are:
1 2 41282 

The factorions for base 10 are:
1 2 145 40585 

The factorions for base 11 are:
1 2 26 48 40472 

The factorions for base 12 are:
1 2

VBScript[edit]

' Factorions - VBScript - PG - 26/04/2020
    Dim fact()
	nn1=9 : nn2=12
	lim=1499999
    ReDim fact(nn2)
	fact(0)=1
	For i=1 To nn2
		fact(i)=fact(i-1)*i
	Next
	For base=nn1 To nn2
		list=""
		For i=1 To lim
			s=0
			t=i
			Do While t<>0
				d=t Mod base
				s=s+fact(d)
				t=t\base
			Loop
			If s=i Then list=list &" "& i
		Next
		Wscript.Echo "the factorions for base "& right(" "& base,2) &" are: "& list
	Next

Output:

the factorions for base  9 are: 1 2 41282
the factorions for base 10 are: 1 2 145 40585
the factorions for base 11 are: 1 2 26 48 40472
the factorions for base 12 are: 1 2

zkl[edit]

Translation of: C

var facts=[0..12].pump(List,fcn(n){ (1).reduce(n,fcn(N,n){ N*n },1) }); #(1,1,2,6....)
fcn factorions(base){
   fs:=List();
   foreach n in ([1..1_499_999]){
      sum,j := 0,n;
      while(j){
	 sum+=facts[j%base];
	 j/=base;
      }
      if(sum==n) fs.append(n);
   }
   fs
}

foreach n in ([9..12]){
   println("The factorions for base %2d are: ".fmt(n),factorions(n).concat("  "));
}

Output:

The factorions for base  9 are: 1  2  41282
The factorions for base 10 are: 1  2  145  40585
The factorions for base 11 are: 1  2  26  48  40472
The factorions for base 12 are: 1  2

Factorions

Contents

360 Assembly[edit]

ALGOL 68[edit]

Applesoft BASIC[edit]

AutoHotkey[edit]

AWK[edit]

C[edit]

C++[edit]

Delphi[edit]

Factor[edit]

Fōrmulæ[edit]

FreeBASIC[edit]

Frink[edit]

Go[edit]

Haskell[edit]

J[edit]

Java[edit]

Julia[edit]

Nim[edit]

OCaml[edit]

Perl[edit]

Phix[edit]

Python[edit]

Racket[edit]

Raku[edit]

REXX[edit]

Ring[edit]

Ruby[edit]

Scala[edit]

Sidef[edit]

Swift[edit]

Wren[edit]

VBScript[edit]

zkl[edit]