IMO 2020 Shortlist N6

For a positive integer n, let dpnq be the number of positive divisors of n, and let ϕpnq be the number of positive integ...

IMO 2020 Shortlist N6

Category: Number Theory

Problem

For a positive integer n, let dpnq be the number of positive divisors of n, and let ϕpnq be the number of positive integers not exceeding n which are coprime to n. Does there exist a constant C such that ϕpdpnqq dpϕpnqq ď C for all n ě 1? (Cyprus)