Question 71
For any positive integer $n$, let $\tau(n)$ denote the number of positive divisors of $n$ and $\varphi(n)$ the number of positive integers not greater than $n$ which are relatively prime to $n$. Find all positive integers $n$ for which one of the three numbers $n$, $\tau(n)$, and $\varphi(n)$ is the arithmetic mean of the other two.