Count the squares in 2020

$a$ should be either even or an odd square integer, in order for $a^a$ to be a square. There are $\frac{2020}{2}=1010$ even integers and $\frac{\lfloor \sqrt{2020}\rfloor}{2} = 22$ odd squares, in the range $1\leq a \leq 2020$ , which add up to $1010+22=1032$