

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


 
   index=: $ #: I.@:,
   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
   (,. ".@:((Num_j_,26}.Alpha_j_) {~ #.inv/)"1) FACTORIONS
 9     1     1
 9     2     2
 9 41282 62558
10     1     1
10     2     2
10   145   145
10 40585 40585
11     1     1
11     2     2
11    26    24
11    48    44
11 40472 28453
12     1     1
12     2     2
 
   NB. tallies of factorions in the bases
   (9+i.4),.+/"1 Q
 9 3
10 4
11 5
12 2
 