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The Number of Relatively Prime Subsets of a Finite Union of Sets of Consecutive Integers
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Mohamed Ayad

Laboratoire de Mathématiques Pures et Appliquées

Université du Littoral

F-62228 Calais

France

Vincenzo Coia

Department of Statistics

University of British Columbia

Vancouver, BC V6T 1Z4

Canada

Omar Kihel

Department of Mathematics

Brock University

St. Catharines, ON L2S 3A1

Canada

**Abstract:**

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*.

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Received November 10 2011;
revised versions received November 11 2011; June 10 2013; September 17 2013; January 27 2014.
Published in *Journal of Integer Sequences*, February 16 2014.

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