Ayad, Mohamed; Coia, Vincenzo; Kihel, Omar The number of relatively prime subsets of a finite union of sets of consecutive integers. (English) Zbl 1285.11006 J. Integer Seq. 17, No. 3, Article 14.3.7, 8 p. (2014). Summary: 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 M. B. Nathanson and B. Orosz [Integers 7, No. 1, A54, 5 p. (2007; Zbl 1159.11010)], M. El Bachraoui [Integers 7, No. 1, A43, 8 p. (2007; Zbl 1139.11005)] and others. We give as well similar formulas for the number of subsets with gcd coprime to \(n\). MSC: 11A25 Arithmetic functions; related numbers; inversion formulas 11B05 Density, gaps, topology 11B75 Other combinatorial number theory 11D41 Higher degree equations; Fermat’s equation Keywords:phi function; relatively prime set; combinatorial identity Citations:Zbl 1159.11010; Zbl 1139.11005 PDFBibTeX XMLCite \textit{M. Ayad} et al., J. Integer Seq. 17, No. 3, Article 14.3.7, 8 p. (2014; Zbl 1285.11006) Full Text: EMIS Online Encyclopedia of Integer Sequences: Number of subsets of {1,2,...,n} with relatively prime elements.