Problem

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

Tags: number theory, function



Let k<<n denote that k<n and kn. Let f:{1,2,...,2013}{1,2,...,M} be such that, if n2013 and k<<n, then f(k)<<f(n). What’s the least possible value of M?