Question 95
Two integers $a, b \in \mathbb{N}^{\star}$ are said to be related if there exists a prime number $p$ such that $a = p b$ or $b = p a$.
Find all integers $n \geqslant 1$ with the following property: one can write all the positive divisors of $n$ ($1$ and $n$ included) exactly once around a circle so that every divisor is related to each of its two neighbours.
Find all integers $n \geqslant 1$ with the following property: one can write all the positive divisors of $n$ ($1$ and $n$ included) exactly once around a circle so that every divisor is related to each of its two neighbours.