Geodesic
Counting tuples restricted by pairwise coprimality conditions
Journal of integer sequences, Tome 18 (2015) no. 10
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 
@article{JIS_2015__18_10_a4,
     author = {Arias de Reyna,  Juan and Heyman,  Randell},
     title = {Counting tuples restricted by pairwise coprimality conditions},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {10},
     zbl = {1329.11102},
     language = {en},
     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/