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MathNet 2001 — Part 01 Question 37

Math Olympiad Vault · MathNet 2001 — Part 01

Question 37

For each positive integer $n$, let $d(n)$ denote the number of all positive divisors of $n$. (Examples: $d(2)=2, d(6)=4, d(9)=3$.)
Determine all positive integers $n$ with the property $(d(n))^3 = 4n$.