  Let n be a non-null positive integer and $d(n)$ is the number of positive
divisors of n, called the divisor function. Of course, $d(n) \leq n$. $d(n) =
1$ if and only if $n = 1$. For $n > 2$ we have $d(n) \geq 2$ and in this paper
we try to find the smallest $k$ such that $d(d(...d(n)...)) = 2$ where the
divisor function is applied $k$ times. At the end of the paper we make a
conjecture based on some observations.
