International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 351-354

An identity for a class of arithmetical functions of two variables

J. Chidambaraswamy and P. V. Krishnaiah

Department of Mathematics, The University of Toledo, Toledo 43606, Ohio , USA

Received 17 November 1986

Copyright © 1988 J. Chidambaraswamy and P. V. Krishnaiah. 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.


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.