Question

145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.
Find the sum of all numbers which are equal to the sum of the factorial
of their digits.
Note: as 1! = 1 and 2! = 2 are not sums they are not included

Answer 1

a quick google search finds that there are 4 such numbers
proofs seem to be by python and brute force
http://mathworld.wolfram.com/Factorion.html