Journal of Integer Sequences, Vol. 18 (2015), Article 15.10.4

Counting Tuples Restricted by Pairwise Coprimality Conditions


Juan Arias de Reyna
Facultad de Matemáticas
Universidad de Sevilla
calle Tarfia, s.n.
41012-Sevilla
Spain

Randell Heyman
School of Mathematics and Statistics
University of New South Wales
Sydney, N.S.W. 2052
Australia

Abstract:

Given a subset A of the set {1, ..., v}2 we say that (a1, ..., av) exhibits pairwise coprimality over A if gcd(ai,aj) = 1 for all (i,j) ∈ A. For a given positive x and a given set A we give an asymptotic formula for the number of (a1, ..., av) with 1 ≤ a1, ..., av ≤ x that exhibit pairwise coprimality over A. This problem has been studied before by Hu.

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(Concerned with sequences A065473 A256390 A256391 A256392.)

Received April 1 2015; revised versions received September 10 2015; September 16 2015. Published in Journal of Integer Sequences, September 16 2015.

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