Consider all integer combinations of $a^b$ for $2\le a\le 5$ and $2\le b\le 5$: $$\begin{array}{rrrr}{2}^2=4,& 2^3=8,& 2^4=16,& 2^5=32\\ 3^2=9,& 3^3=27,& 3^4=81,& 3^5=243\\ 4^2=16,& 4^3=64,& 4^4=256,& 4^5=1024\\ 5^2=25,& 5^3=125,& 5^4=625,& 5^5=3125\end{array}$$

If they are then placed in numerical order, with any repeats removed, we get the following sequence of $15$ distinct terms: $$4,8,9,16,25,27,32,64,81,125,243,256,625,1024,3125.$$

How many distinct terms are in the sequence generated by $a^b$ for $2\le a\le 100$ and $2\le b\le 100$?