

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


with javascript_semantics
for base=9 to 12 do
    printf(1,"The factorions for base %d are: ", base)
    for i=1 to 1499999 do
        atom total = 0, j = i, d
        while j>0 and total<=i do
            d = remainder(j,base)
            total += factorial(d)
            j = floor(j/base)
        end while
        if total==i then printf(1,"%d ", i) end if
    end for
    printf(1,"\n")
end for
