NL-BXMO-TST 2020 Problem 1

For an integer $n \ge 3$ we consider a circle with $n$ points on it. We place a positive integer at each point, where the numbers are not necessary need to be different. Such placement of numbers is called stable as three numbers next to always have product $n$ each other. For how many values of $n$ with $3 \le n \le 2020$ is it possible to place numbers in a stable way?