Competition problem — Number theory

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Number theory Difficulty 5.5 AIME, harder Find the answer

15. Find all positive integers $n$ such that the product of all divisors of $n$ other than $n$ is exactly $n^{2}$ . (These integers are multiplicative analogues of perfect numbers.)

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.