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2019 A/NT2: Fraction is Not an Integer

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January 27, 2019
2019number theory

Problem Statement

For all positive integers nn, let f(n)f(n) return the smallest positive integer kk for which nk\tfrac{n}{k} is not an integer. For example, f(6)=4f(6) = 4 because 11, 22, and 33 all divide 66 but 44 does not. Determine the largest possible value of f(n)f(n) as nn ranges over the set {1,2,…,3000}\{1,2,\ldots, 3000\}.
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