What a Coincidence!

Let $s(n)$ denote the number of positive integers $k$ less than or equal to $n$ such that for all positive integers $d$ satisfying $1 < d < k$ , we have $d^2 \not| k$ . Let $t(n)$ denote the number of positive integers $k$ less than or equal to $n$ such that $\gcd(k, n) = 1$ . Find the least positive integer $a$ such that $20s(a) - t(20.13a) = 0$