An Euler problem: How many of these numbers are of the form $a^b$?

Question

How much numbers can be written in the form $a^b$, where $a$ and $b$ are integers that are between $2$ and $100$?

How can I start this problem? Any hints please?

Thanks!

Answer 1

For $2\le a^b\le 100,$ if you let $b=1,2,\cdots$, what kind of condition of $a$ can you get?