The Repeated Divisor Function and Possible Correlation with Highly Composite Numbers

2017/03/31 by Chakrabarty, Sayak, Dutta, Arghya
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.1704.00007

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) ≤ n. d(n) = 1 if and only if n = 1. For n > 2 we have d(n) ≥ 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.

Related

• Repeated values of some restricted divisor functions
• Highly Composite Numbers
• New upper bounds for the number of divisors function
• Some Properties and Applications of Non-trivial Divisor Functions
• Correlations of the von Mangoldt and higher divisor functions II. Divisor correlations in short ranges