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# Factorions

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

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 talk page) that no factorion in base 10 can exceed   1,499,999.

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)

## 11l

Translation of: Python
`V fact = [1]L(n) 1..11   fact.append(fact[n-1] * n) L(b) 9..12   print(‘The factorions for base ’b‘ are:’)   L(i) 1..1'499'999      V fact_sum = 0      V j = i      L j > 0         V d = j % b         fact_sum += fact[d]         j I/= b      I fact_sum == i         print(i, end' ‘ ’)   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

```

## 360 Assembly

`*        Factorions                26/04/2020FACTORIO 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 saveNN1      EQU    9                  nn1=9NN2      EQU    12                 nn2=12LIM      DC     f'1499999'         lim=1499999FACT     DC     (NN2+1)F'1'        fact(0:12)PG       DS     CL80               bufferPGX      DC     CL80'Base .. : '   buffer initXDEC     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

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 ) )    ODEND`
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

`100 DIM FACT(12)110 FACT(0) = 1120 FOR N = 1 TO 11130     FACT(N) = FACT(N - 1) * N140 NEXT 200 FOR B = 9 TO 12210     PRINT "THE FACTORIONS ";215     PRINT "FOR BASE "B" ARE:"220     FOR I = 1 TO 1499999230         SUM = 0240         FOR J = I TO 0 STEP 0245             M =  INT (J / B)250             D = J - M * B260             SUM = SUM + FACT(D)270             J = M280         NEXT J290         IF SU = I THEN  PRINT I" ";300     NEXT I310     PRINT : PRINT 320 NEXT B`

## Arturo

`factorials: [1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800] factorion?: function [n, base][    try? [        n = sum map digits.base:base n 'x -> factorials\[x]    ]    else [        print ["n:" n "base:" base]        false    ]] loop 9..12 'base ->    print ["Base" base "factorions:" select 1..45000 'z -> factorion? z base]]`
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]```

## AutoHotkey

Translation of: C
`fact:=[]fact[0] := 1while (A_Index < 12)	fact[A_Index] := fact[A_Index-1] * A_Indexb := 9while (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 % resreturn`
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

` # syntax: GAWK -f FACTORIONS.AWK# converted from CBEGIN {    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

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++

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
```

## Common Lisp

`(defparameter *bases* '(9 10 11 12))(defparameter *limit* 1500000) (defun ! (n) (apply #'* (loop for i from 2 to n collect i))) (defparameter *digit-factorials* (mapcar #'! (loop for i from 0 to (1- (apply #'max *bases*)) collect i))) (defun fact (n) (nth n *digit-factorials*)) (defun digit-value (digit)  (let ((decimal (digit-char-p digit)))    (cond ((not (null decimal)) decimal)          ((char>= #\Z digit #\A) (+ (char-code digit) (- (char-code #\A)) 10))          ((char>= #\z digit #\a) (+ (char-code digit) (- (char-code #\a)) 10))          (t nil)))) (defun factorionp (n &optional (base 10))  (= n (apply #'+            (mapcar #'fact                    (map 'list #'digit-value                         (write-to-string n :base base)))))) (loop for base in *bases* do  (let ((factorions        (loop for i from 1 while (< i *limit*) if (factorionp i base) collect i)))    (format t "In base ~a there are ~a factorions:~%" base (list-length factorions))    (loop for n in factorions do      (format t "~c~a" #\Tab (write-to-string n :base base))      (if (/= base 10) (format t " (decimal ~a)" n))      (format t "~%"))    (format t "~%")))`
Output:
```In base 9 there are 3 factorions:
1 (decimal 1)
2 (decimal 2)
62558 (decimal 41282)

In base 10 there are 4 factorions:
1
2
145
40585

In base 11 there are 5 factorions:
1 (decimal 1)
2 (decimal 2)
24 (decimal 26)
44 (decimal 48)
28453 (decimal 40472)

In base 12 there are 2 factorions:
1 (decimal 1)
2 (decimal 2)
```

## Delphi

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.`

## F#

` //  Factorians. Nigel Galloway: October 22nd., 2021let N=[|let mutable n=1 in yield n; for g in 1..11 do n<-n*g; yield n|]let fG n g=let rec fN g=function i when i<n->g+N.[i] |i->fN(g+N.[i%n])(i/n) in fN 0 g {9..12}|>Seq.iter(fun n->printf \$"In base %d{n} Factorians are:"; {1..1500000}|>Seq.iter(fun g->if g=fG n g then printf \$" %d{g}"); printfn "") `
Output:
```In base 9 Factorians are: 1 2 41282
In base 10 Factorians are: 1 2 145 40585
In base 11 Factorians are: 1 2 26 48 40472
In base 12 Factorians are: 1 2
```

## Factor

`USING: formatting io kernel math math.parser math.ranges memoizeprettyprint sequences ;IN: rosetta-code.factorions ! Memoize factorial functionMEMO: 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

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.

## FreeBASIC

`Dim As Integer fact(12), suma, d, jfact(0) = 1For n As Integer = 1 To 11    fact(n) = fact(n-1) * nNext nFor 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 : PrintNext bSleep`
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

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

## Go

`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
```

`import Text.Printf (printf)import Data.List (unfoldr)import Control.Monad (guard) factorion :: Int -> Int -> Boolfactorion 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

`    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 6255810     1     110     2     210   145   14510 40585 4058511     1     111     2     211    26    2411    48    4411 40472 2845312     1     112     2     2    NB. tallies of factorions in the bases   (9+i.4),.+/"1 Q 9 310 411 512 2 `

## Java

` 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

`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]
```

## Mathematica / Wolfram Language

`ClearAll[FactorionQ]FactorionQ[n_,b_:10]:=Total[IntegerDigits[n,b]!]==nSelect[Range[1500000],FactorionQ[#,9]&]Select[Range[1500000],FactorionQ[#,10]&]Select[Range[1500000],FactorionQ[#,11]&]Select[Range[1500000],FactorionQ[#,12]&]`
Output:
```{1, 2, 41282}
{1, 2, 145, 40585}
{1, 2, 26, 48, 40472}
{1, 2}```

## Nim

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

`from math import facfrom 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

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`

## Pascal

modified munchhausen numbers#Pascal. output in base and 0! == 1!, so in Base 10 40585 has the same digits as 14558.

`program munchhausennumber;{\$IFDEF FPC}{\$MODE objFPC}{\$Optimization,On,all}{\$ELSE}{\$APPTYPE CONSOLE}{\$ENDIF}uses  sysutils;type  tdigit  = byte;const  MAXBASE = 17; var  DgtPotDgt : array[0..MAXBASE-1] of NativeUint;  dgtCnt : array[0..MAXBASE-1] of NativeInt;  cnt: NativeUint; function convertToString(n:NativeUint;base:byte):AnsiString;const  cBASEDIGITS = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvxyz';var  r,dgt: NativeUint;begin  IF base > length(cBASEDIGITS) then    EXIT('Base to big');  result := '';  repeat    r := n div base;    dgt := n-r*base;    result := cBASEDIGITS[dgt+1]+result;    n := r;  until n =0;end; function CheckSameDigits(n1,n2,base:NativeUInt):boolean;var   i : NativeUInt;Begin  fillchar(dgtCnt,SizeOf(dgtCnt),#0);  repeat    //increment digit of n1    i := n1;n1 := n1 div base;i := i-n1*base;inc(dgtCnt[i]);    //decrement digit of n2    i := n2;n2 := n2 div base;i := i-n2*base;dec(dgtCnt[i]);  until (n1=0) AND (n2= 0);  result := true;  For i := 2 to Base-1 do    result := result AND (dgtCnt[i]=0);  result := result AND (dgtCnt[0]+dgtCnt[1]=0); end; procedure Munch(number,DgtPowSum,minDigit:NativeUInt;digits,base:NativeInt);var  i: NativeUint;  s1,s2: AnsiString;begin  inc(cnt);  number := number*base;  IF digits > 1 then  Begin    For i := minDigit to base-1 do      Munch(number+i,DgtPowSum+DgtPotDgt[i],i,digits-1,base);  end  else    For i := minDigit to base-1 do      //number is always the arrangement of the digits leading to smallest number      IF (number+i)<= (DgtPowSum+DgtPotDgt[i]) then        IF CheckSameDigits(number+i,DgtPowSum+DgtPotDgt[i],base) then          iF number+i>0 then          begin            s1 := convertToString(DgtPowSum+DgtPotDgt[i],base);            s2 := convertToString(number+i,base);            If length(s1)= length(s2) then              writeln(Format('%*d %*s  %*s',[Base-1,DgtPowSum+DgtPotDgt[i],Base-1,s1,Base-1,s2]));          end;end; //factorionsprocedure InitDgtPotDgt(base:byte);var  i: NativeUint;Begin  DgtPotDgt[0]:= 1;  For i := 1 to Base-1 do    DgtPotDgt[i] := DgtPotDgt[i-1]*i;  DgtPotDgt[0]:= 0;end;{//Munchhausen numbersprocedure InitDgtPotDgt;var  i,k,dgtpow: NativeUint;Begin  // digit ^ digit ,special case 0^0 here 0  DgtPotDgt[0]:= 0;  For i := 1 to Base-1 do  Begin    dgtpow := i;    For k := 2 to i do      dgtpow := dgtpow*i;    DgtPotDgt[i] := dgtpow;  end;end;}var  base : byte;begin  cnt := 0;  For base := 2 to MAXBASE do  begin    writeln('Base = ',base);    InitDgtPotDgt(base);    Munch(0,0,0,base,base);  end;  writeln('Check Count ',cnt);end.`
Output:
```TIO.RUN Real time: 45.701 s User time: 44.968 s Sys. time: 0.055 s CPU share: 98.51 %
Base = 2
1 1  1
Base = 3
1  1   1
2  2   2
Base = 4
1   1    1
2   2    2
7  13   13
Base = 5
1    1     1
2    2     2
49  144   144
Base = 6
1     1      1
2     2      2
25    41     14
26    42     24
Base = 7
1      1       1
2      2       2
Base = 8
1       1        1
2       2        2
Base = 9
1        1         1
2        2         2
41282    62558     25568
Base = 10
1         1          1
2         2          2
145       145        145
40585     40585      14558
Base = 11
1          1           1
2          2           2
26         24          24
48         44          44
40472      28453       23458
Base = 12
1           1            1
2           2            2
Base = 13
1            1             1
2            2             2
519326767     83790C5B      135789BC
Base = 14
1             1              1
2             2              2
12973363226     8B0DD409C      11489BCDD
Base = 15
1              1               1
2              2               2
1441            661             166
1442            662             266
Base = 16
1               1                1
2               2                2
2615428934649     260F3B66BF9      1236669BBFF
Base = 17
1                1                 1
2                2                 2
40465             8405              1458
43153254185213     146F2G8500G4      111244568FGG
43153254226251     146F2G8586G4      124456688FGG
Check Count 1571990934
```

## Perl

### Raku version

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```

### Sidef version

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

Translation of: C

As per talk page (ok, and the task description), this is incorrectly using the base 10 limit for bases 9, 11, and 12.

```with javascript_semantics
for base=9 to 12 do
printf(1,"The factorions for base %d are: ", base)
for i=1 to 1499999 do
atom total = 0, j = i, d
while j>0 and total<=i do
d = remainder(j,base)
total += factorial(d)
j = floor(j/base)
end while
if total==i then printf(1,"%d ", i) end if
end for
printf(1,"\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
```
Translation of: Sidef

Using the correct limits and much faster, or at least it was until I upped the bases to 14.

```with javascript_semantics
function max_power(integer base = 10)
integer m = 1
atom f = factorial(base-1)
while m*f >= power(base,m-1) do
m += 1
end while
return m-1
end function

constant digits = "0123456789abcd"

function fcomb(sequence res, integer base, n, at=1, atom fsum=0, string chosen="")
if length(chosen)=n then
string fs = sort(sprintf("%a",{{base,fsum}}))
if fs=chosen then
res = append(res,sprintf("%d",fsum))
end if
else
for i=at to base do
res = fcomb(res,base,n,i,fsum+factorial(i-1),chosen&digits[i])
end for
end if
return res
end function

function factorions(integer base = 10)
sequence result = {}
for k=1 to max_power(base) do
result &= fcomb({},base,k)
end for
return result
end function

for base=2 to 14 do
printf(1,"Base %2d factorions: %s\n",{base,join(factorions(base))})
end for
```
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
Base 13 factorions: 1 2 519326767
Base 14 factorions: 1 2 12973363226
```

It will in fact go all the way to 17, though I don't recommend it:

```Base 15 factorions: 1 2 1441 1442
Base 16 factorions: 1 2 2615428934649
Base 17 factorions: 1 2 40465 43153254185213 43153254226251
```

## PureBasic

Translation of: C
`Declare main() If OpenConsole() : main() : Else : End 1 : EndIfInput() : End Procedure main()  Define.i n,b,d,i,j,sum  Dim fact.i(12)   fact(0)=1  For n=1 To 11 : fact(n)=fact(n-1)*n : Next   For b=9 To 12    PrintN("The factorions for base "+Str(b)+" are: ")    For i=1 To 1500000-1      sum=0 : j=i      While j>0        d=j%b : sum+fact(d) : j/b      Wend      If sum=i : Print(Str(i)+" ") : EndIf    Next    Print(~"\n\n")  NextEndProcedure`
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

Translation of: C
`fact = [1] # cache factorials from 0 to 11for 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(1, 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("\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
```

## Quackery

`  [ table ]              is results   (   n --> s )  4 times     [ ' [ stack [ ] ]      copy      ' results put ]   [ results dup take     rot join swap put ]  is addresult ( n n -->   )   [ table 9 10 11 12 ]   is radix     (   n --> n )   [ table 1 ]            is !         (   n --> n )       1 11 times    [ i^ 1+ * dup      ' ! put ]  drop    [ dip dup    0 temp put    [ tuck /mod !      temp tally      swap over 0 =       until ]    2drop     temp take = ]       is factorion ( n n --> b )   1500000 times    [ i^ 4 times       [ dup         i^ radix        factorion if          [ dup i^             addresult ] ]      drop ]  4 times     [ say "Factorions for base "     i^ radix echo say ": "     i^ results take echo cr ]`
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 ]
```

## Racket

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

(formerly Perl 6)

Works with: Rakudo version 2019.07.1
`constant @factorial = 1, |[\*] 1..*; constant \$limit = 1500000; constant \$bases = 9 .. 12; my @result; \$bases.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

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
```

## Ruby

` 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

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

`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

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```

## Vlang

Translation of: Go
`import strconv fn main() {    // cache factorials from 0 to 11    mut fact := [12]u64{}    fact[0] = 1    for n := u64(1); n < 12; n++ {        fact[n] = fact[n-1] * n    }     for b := 9; b <= 12; b++ {        println("The factorions for base \$b are:")        for i := u64(1); i < 1500000; i++ {            digits := strconv.format_uint(i, b)            mut sum := u64(0)            for digit in digits {                if digit < `a` {                    sum += fact[digit-`0`]                } else {                    sum += fact[digit+10-`a`]                }            }            if sum == i {                print("\$i ")            }        }        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
```

## Wren

Translation of: C
`// cache factorials from 0 to 11var fact = List.filled(12, 0)fact[0] = 1for (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

`' 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

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
```