Question 20
Let $a$ be a positive integer. Denote by $\tau(a)$ and $\varphi(a)$ respectively the number of all positive integers that divide $a$ and the number of all positive integers not greater than $a$ and relatively prime to $a$. Find all positive integers $n$ having only two prime divisors and such that $\varphi(\tau(n)) = \tau(\varphi(n))$.