$k$-Pretty Numbers

Call a positive integer $n$ $k$-pretty if $n$ is divisible by $k$ and $n$ has exactly $k$ positive divisors. For example, $18$ is $6$-pretty: it is divisible by $6$, and its divisors are $1, 2, 3, 6, 9, 18$ — exactly six of them. Let $S$ be the sum of all $20$-pretty positive integers not exceeding $2019$. Find $\tfrac{S}{20}$.