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Integers


Mathematical Citation Quotient (MCQ) 2017: 0.20

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1867-0660
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The Number of Relatively Prime Subsets of {1, 2, . . . , n}

Mohamed Ayad
  • Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral, F6228 Calais, France. E-mail:
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/ Omar Kihel
  • Department of Mathematics, Brock University, St. Catharines, L2S 3A1 Ontario, Canada. E-mail:
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Published Online: 2009-06-15 | DOI: https://doi.org/10.1515/INTEG.2009.015

Abstract

A nonempty subset A ⊆ {1, 2, . . . , n} is relatively prime if gcd(A) = 1. Let ƒ(n) denote the number of relatively prime subsets of {1, 2, . . . , n}. The sequence given by the values of ƒ(n) is sequence A085945 in Sloane's On-Line Encyclopedia of Integer Sequences. In this article we show that ƒ(n) is never a square if n ≥ 2. Moreover, we show that reducing the terms of this sequence modulo any prime l ≠ 3 leads to a sequence which is not periodic modulo l.

Keywords.: Relatively prime sets; sequence mod p; squares in a sequence

About the article

Received: 2008-07-11

Revised: 2009-02-27

Accepted: 2009-03-11

Published Online: 2009-06-15

Published in Print: 2009-06-01


Citation Information: Integers, Volume 9, Issue 2, Pages 163–166, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/INTEG.2009.015.

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[1]
Mohamed El Bachraoui and Florian Luca
Quaestiones Mathematicae, 2012, Volume 35, Number 2, Page 235

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