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.

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


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, ..., avx 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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