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arXiv · 1704.00007

The Repeated Divisor Function and Possible Correlation with Highly Composite Numbers

Sayak Chakrabarty·Arghya Dutta
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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, $d(n) \leq n$. $d(n) = 1$ 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.

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Sayak Chakrabarty, Arghya Dutta. 2017-03-31. The Repeated Divisor Function and Possible Correlation with Highly Composite Numbers. https://arxiv.org/abs/1704.00007

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