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!).