On a Diophantine equation of Ayad and Kihel

Mohamed El Bachraoui, Florian Luca

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Let f(n) denote the number of relatively prime sets in {1,..., n}. This is sequence A085945 in Sloane's On-Line Encyclopedia of Integer Sequences. Motivated by a paper of Ayad and Kihel [1], we show that there are at most finitely many positive integers n such that f(n) is a perfect power of exponent > 1 of some other integer. We also show that the sequence {f(n)} n≥1 is not holonomic; that is, it satisfies no recurrence relation of finite order with polynomial coefficients.

Original languageEnglish
Pages (from-to)235-243
Number of pages9
JournalQuaestiones Mathematicae
Issue number2
Publication statusPublished - Jun 2012


  • Prime subsets
  • holonomic sequences
  • perfect powers

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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