CMO 2018 Problem 3

Two positive integers $a$ and $b$ are prime-related if $a=p b$ or $b=p a$ for some prime $p$. Find all positive integers $n$, such that $n$ has at least three divisors, and all the divisors can be arranged without repetition in a circle so that any two adjacent divisors are prime-related.

Note that 1 and $n$ are included as divisors.