AN IDENTITY FOR A CLASS OF ARITHMETICAL FUNCTIONS OF TWO VARIABLES

J. CHIDAMBARASWAMY ； P.V. KRISHNAIAH

《International Journal of Mathematics and Mathematical Sciences》 1988卷 (1988/12) Pp. 351-354

https://doi.org/10.1155/S0161171288000419

摘要

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 (*) (The equation is abbreviated) 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.

關鍵字

Arithmetical functions of two variables and multiplicativity in both variables ； Ramanujan's sum and its generalizations