Question 94
Let $f: \mathbb{N}^{\star} \rightarrow \mathbb{N}^{\star}$ be a function such that for every integer $n \geqslant 1$, $f(f(n))$ is equal to the number of positive divisors of $n$. Prove that if $p$ is a prime number, then $f(p)$ is also a prime number.