Number of $X$ expressible in the form $a^3 \cdot b$

Question

A positive integer X is said to be a cube-loving number if it can be written as $(a^3) \cdot b$, for some positive integers $a$ and $b$ ($a>1$,$b \ge 1$). Given a positive integer $n$, determine the number of Cube-loving numbers less than or equal to $n$.

Answer 1

Hint: the Cube-loving numbers are exactly those numbers divisible by $p^3$ where $p$ is a prime.

Answer 2

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