A factorion is an integer which is equal to the sum of factorials of its digits. There are exactly four such numbers: 1 | = | 1! 2 | = | 2! 145 | = | 1! + 4! + 5! 40585 | = | 4! + 0! + 5! + 8! + 5! (OEIS A014080; Gardner 1978, Madachy 1979, Pickover 1995). Obviously, the factorion of an n-digit number cannot exceed n·9!.

factorial | factorial sums