

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


// 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")
}