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