Sums of products of generalized Ramanujan sums

Soichi Ikeda, Isao Kiuchi, Kaneaki Matsuoka

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


We consider weighted averages for the products t(1) k1 (j) … t(n) kn (j) of generalized Ramanujan sums t(i) ki (j) = ∑d| gcd(ki, j) fi(d)gi(ki/d)hi(j/d) with any arithmetical functions fi, gi and hi (i = 1, …, n), and derive formulas for several weighted averages with weights concerning completely multiplicative functions, completely additive functions, and others.

Original languageEnglish
Article number16.2.7
JournalJournal of Integer Sequences
Issue number2
Publication statusPublished - 2016 Mar 18


  • Arithmetical function
  • Greatest common divisor
  • Ramanujan’s sum

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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