On A Divisor Sum Involving Pairwise Relatively Prime Positive Integers

2019/09/15 by Masum Billal, Billal, Masum
Mathematics · #11A25 #11B75 #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Mathematics and Applications #math.GM #msc:11A25 #msc:11B75

paper · pdf · doi:10.48550/arxiv.1909.07823

10 pages

openalex publication_date 2019/09/15 · arxiv created 2021/08/23 · arxiv updated 2021/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The number of tuples with positive integers pairwise relatively prime to each other with product at most n is considered. A generalization of μ² where μ is the Möbius 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.

Related

• On almost-prime k-tuples
• Divisor Functions and the Number of Sum Systems
• Relatively Prime Sets, Divisor Sums, and Partial Sums
• Arithmetic properties of the sum of divisors
• A Divisor Function Inequality