

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.



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


#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;
}