Geodesic
Counting tuples restricted by pairwise coprimality conditions
Journal of integer sequences, Tome 18 (2015) no. 10.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Given a subset $A$ of the set ${1, \dots , v}^{2}$ we say that $(a_{1}, \dots , a_{v})$ exhibits pairwise coprimality over $A$ if $gcd(a_{i},a_{j}) = 1$ for all $(i,j) \in A$. For a given positive $x$ and a given set $A$ we give an asymptotic formula for the number of $(a_{1}, \dots , a_{v})$ with $1 \le a_{1}, \dots , a_{v} \le x$ that exhibit pairwise coprimality over $A$. This problem has been studied before by Hu.
Classification : 11N25, 11N36, 11N37, 11A25
Keywords: pairwise coprimality, arithmetic function 
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     author = {Arias de Reyna, Juan and Heyman, Randell},
     title = {Counting tuples restricted by pairwise coprimality conditions},
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     number = {10},
     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a4/}
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Arias de Reyna, Juan; Heyman, Randell. Counting tuples restricted by pairwise coprimality conditions. Journal of integer sequences, Tome 18 (2015) no. 10. http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a4/