IMO 2021 Shortlist N3

Find all positive integers n with the following property: the k positive divisors of n have a permutation pd1,d2,...,dkq...

IMO 2021 Shortlist N3

Category: Number Theory

Problem

Find all positive integers n with the following property: the k positive divisors of n have a permutation pd1,d2,...,dkq such that for every i “1,2,...,k, the number d1 ¨¨¨di is a perfect square.