# Problem 254: Sums of Digit Factorials
Define f(n) as the sum of the factorials of the digits of n. For
example, f(342) = 3! + 4! + 2! = 32. Define sf(n) as the sum of the
digits of f(n). So sf(342) = 3 + 2 = 5. Define g(i) to be the smallest
positive integer n such that sf(n) = i. Though sf(342) is 5, sf(25) is
also 5, and it can be verified that g(5) is 25. Define sg(i) as the sum
of the digits of g(i). So sg(5) = 2 + 5 = 7. Further, it can be verified
that g(20) is 267 and ∑ sg(i) for 1 ≤ i ≤ 20 is 156. What is ∑ sg(i) for
1 ≤ i ≤ 150?