

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


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")