Question 91
Let $a_{1}, a_{2}, \ldots, a_{n}, \ldots$ be a sequence of positive integers such that $a_{i+1}$ is the number of positive divisors of $a_{i}$ for every $i \geq 1$. Suppose that $a_{2} \neq 2$. Prove that there exists an index $m$ such that $a_{m}$ is a perfect square.