On A Divisor Sum Involving Pairwise Relatively Prime Positive Integers

Masum Billal

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arXiv · 1909.07823

On A Divisor Sum Involving Pairwise Relatively Prime Positive Integers

Masum Billal

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Abstract

The number of tuples with positive integers pairwise relatively prime to each other with product at most $n$ is considered. A generalization of $\mu^{2}$ where $\mu$ is the M\"{o}bius function is used to formulate this divisor sum and establish some identities. One such identity is a weighted sum of reciprocal of square-free numbers not exceeding $n$. Some auxiliary number theoretic functions are introduced to formulate this sum.

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Masum Billal. 2019-09-15. On A Divisor Sum Involving Pairwise Relatively Prime Positive Integers. https://arxiv.org/abs/1909.07823

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