Pairwise Relative Primality of Positive Integers

Abstract

Given a graph $G=(V,E)$ with $V=\{1,2,...,k\}$, the $k$ positive integers $a_1,a_2,...,a_k$ are $G$-wise relatively prime if $(a_i,a_j)=1$ for $\{i,j\}\in E$. In this note we consider the problem of finding the probability $A_G$ that k positive integers are $G$-wise relatively prime. As an application of our results, we solve the problems of finding probabilities that k positive integers have exact (or at least) r relatively prime pairs, which was proposed by P. Moree.

References in corpus (2)

• Asymptotic normality and greatest common divisors
• Counting carefree couples

Cited by in corpus (6)

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• Counting $r$-tuples of positive integers with $k$-wise relatively prime components
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• On the reciprocal sum of lcm of k-tuples
• The Density of Tuples Restricted by Relatively r-Prime Conditions
• Errata and Addenda to Mathematical Constants