Sums of products of generalized Ramanujan sums

Soichi Ikeda, Isao Kiuchi, Kaneaki Matsuoka

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume19
Issue number2
Publication statusPublished - 2016 Mar 18

Keywords

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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Ikeda, S., Kiuchi, I., & Matsuoka, K. (2016). Sums of products of generalized Ramanujan sums. Journal of Integer Sequences, 19(2), [16.2.7].

Sums of products of generalized Ramanujan sums. / Ikeda, Soichi; Kiuchi, Isao; Matsuoka, Kaneaki.

In: Journal of Integer Sequences, Vol. 19, No. 2, 16.2.7, 18.03.2016.

Research output: Contribution to journalArticle

Ikeda, S, Kiuchi, I & Matsuoka, K 2016, 'Sums of products of generalized Ramanujan sums', Journal of Integer Sequences, vol. 19, no. 2, 16.2.7.
Ikeda S, Kiuchi I, Matsuoka K. Sums of products of generalized Ramanujan sums. Journal of Integer Sequences. 2016 Mar 18;19(2). 16.2.7.
Ikeda, Soichi ; Kiuchi, Isao ; Matsuoka, Kaneaki. / Sums of products of generalized Ramanujan sums. In: Journal of Integer Sequences. 2016 ; Vol. 19, No. 2.
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