Numbers of the form $a^2b^3$

 Published on Saturday, 11th August 2018, 04:00 pm; Solved by 533;
Difficulty rating: 40%

Problem 634

Define $F(n)$ to be the number of integers $x≤n$ that can be written in the form $x=a^2b^3$, where $a$ and $b$ are integers not necessarily different and both greater than 1.

For example, $32=2^2\times 2^3$ and $72=3^2\times 2^3$ are the only two integers less than 100 that can be written in this form. Hence, $F(100)=2$.

Further you are given $F(2\times 10^4)=130$ and $F(3\times 10^6)=2014$.

Find $F(9\times 10^{18})$.