Repeating tau function

For each positive integer $n$, let $\tau(n)$ denote the number of positive divisors of $n$. Let $S$ be the set of all positive integers $n$ such that $n$ is divisible by $3$ but not divisible by $81$, and the sequence $$\tau(n),\ \tau(\tau(n)),\ \tau(\tau(\tau(n))),\ \ldots$$ does not contain any perfect square. Find the sum of all elements of $S$.