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Factorisation triples

Problem 418

Published on Saturday, 9th March 2013, 07:00 pm; Solved by 346

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!).