Jump to ContentJump to Main Navigation
Show Summary Details
More options …



Mathematical Citation Quotient (MCQ) 2017: 0.20

See all formats and pricing
More options …

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:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Omar Kihel
  • Department of Mathematics, Brock University, St. Catharines, L2S 3A1 Ontario, Canada. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2009-06-15 | DOI: https://doi.org/10.1515/INTEG.2009.015


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.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

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

Comments (0)

Please log in or register to comment.
Log in