The Repeated Divisor Function and Possible Correlation with Highly Composite Numbers

Abstract

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, $d(n)\le n$. $d(n)=1$ if and only if $n=1$. For $n>2$ we have $d(n)\ge 2$ 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.

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