Geodesic
The number of relatively prime subsets of a finite union of sets of consecutive integers
Journal of integer sequences, Tome 17 (2014) no. 3
Let $A$ be a finite union of disjoint sets of consecutive integers and let $n$ be a positive integer. We give a formula for the number of relatively prime subsets (resp., relatively prime subsets of cardinality $k$) of $A$, which generalizes results of Nathanson, El Bachraoui and others. We give as well similar formulas for the number of subsets with gcd coprime to $n$.
Keywords: phi function, relatively prime set, combinatorial identity 
@article{JIS_2014__17_3_a4,
     author = {Ayad,  Mohamed and Coia,  Vincenzo and Kihel,  Omar},
     title = {The number of relatively prime subsets of a finite union of sets of consecutive integers},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {3},
     zbl = {1285.11006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_3_a4/}
}
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Ayad,  Mohamed; Coia,  Vincenzo; Kihel,  Omar. The number of relatively prime subsets of a finite union of sets of consecutive integers. Journal of integer sequences, Tome 17 (2014) no. 3. http://geodesic.mathdoc.fr/item/JIS_2014__17_3_a4/