An identity for a class of arithmetical functions of two variables
J. Chidambaraswamy, P. V. Krishnaiah · International Journal of Mathematics and Mathematical Sciences · 1988
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 urn:x-wiley:01611712:media:ijmm180307:ijmm180307-math-0001 according 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.