International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1988 / Article

Open Access

Volume 11 |Article ID 180307 | https://doi.org/10.1155/S0161171288000419

J. Chidambaraswamy, P. V. Krishnaiah, "An identity for a class of arithmetical functions of two variables", International Journal of Mathematics and Mathematical Sciences, vol. 11, Article ID 180307, 4 pages, 1988. https://doi.org/10.1155/S0161171288000419

An identity for a class of arithmetical functions of two variables

Received17 Nov 1986

Abstract

For a positive integer r, let r denote the quotient of r by its largest squarefree divisor (1=1). Recently, K. R. Johnson proved that()d|n|C(d,r)|=rpanrp+r(a+1)panrp|r(a(p1)+1)or0according as r|n or not where C(n,r) is the well known Ramanujan's sum. In this paper, using a different method, we generalize () to a wide class of arithmetical functions of 2 variables and deduce as special cases () and similar formulae for several generalizations of Ramanujan''s sum.

Copyright © 1988 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views69
Downloads315
Citations

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.