Problem

Source: 2021 Turkey JBMO TST 2021 P5

Tags: number theory, number theory proposed, function



$d(n)$ shows the number of positive integer divisors of positive integer $n$. For which positive integers $n$ one cannot find a positive integer $k$ such that $\underbrace{d(\dots d(d}_{k\ \text{times}} (n) \dots )$ is a perfect square.