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MathNet 2018-part-02 — 181 problems (EN–VI) Question 3

Math Olympiad Vault · MathNet 2018-part-02 — 181 problems (EN–VI)

Question 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.