# Problem 418: Factorisation triples
Let n be a positive integer. An integer triple (a, b, c) is called a
factorisation triple of n if: 1 ≤ a ≤ b ≤ c a·b·c = n. Define f(n) to be
a + b + c for the factorisation triple (a, b, c) of n which minimises c
/ a. One can show that this triple is unique. For example, f(165) = 19,
f(100100) = 142 and f(20!) = 4034872. Find f(43!).