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Problem 895

AIME late

Number theory Difficulty 5.7 Find the answer

[39.3] For any positive integer $n$ , let $d(n)$ denote the number of all positive divisors of $n$ (including 1 and $n$ ). Determine all possible positive integers $k$ such that there exists a positive integer $n$ satisfying
$d\left(n^{2}\right) / d(n)=k$

Your answer

Official solution

None

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None

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