

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


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)
 