MathNet 2018-part-01 — 181 problems (EN–VI) Question 15

For $n \in \mathbb{N}$ let $D_2(n)$ (respectively $D_3(n)$) denote the number of divisors of $n$ that are perfect squares (respectively perfect cubes). Prove that there is an $n$ such that $D_2(n) = 999D_3(n)$.