

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


' Factorions - VBScript - PG - 26/04/2020
    Dim fact()
	nn1=9 : nn2=12
	lim=1499999
    ReDim fact(nn2)
	fact(0)=1
	For i=1 To nn2
		fact(i)=fact(i-1)*i
	Next
	For base=nn1 To nn2
		list=""
		For i=1 To lim
			s=0
			t=i
			Do While t<>0
				d=t Mod base
				s=s+fact(d)
				t=t\base
			Loop
			If s=i Then list=list &" "& i
		Next
		Wscript.Echo "the factorions for base "& right(" "& base,2) &" are: "& list
	Next 