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Problem 4 of Second round

Source: IV International Festival of Young Mathematicians Sozopol 2013, Theme for 10-12 grade

January 22, 2020
number theoryfunction

Problem Statement

Let k<<nk<<n denote that k<nk<n and k∣nk\mid n. Let f:{1,2,...,2013}→{1,2,...,M}f:\{1,2,...,2013\}\rightarrow \{1,2,...,M\} be such that, if n≤2013n\leq 2013 and k<<nk<<n, then f(k)<<f(n)f(k)<<f(n). What’s the least possible value of MM?
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