International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 37, Pages 2335-2344
doi:10.1155/S0161171203301139
Some characterizations of specially multiplicative functions
Pentti Haukkanen
Department of Mathematics, Statistics and Philosophy, University of Tampere, FIN-33014, Finland
Abstract
A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function fA such that f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d) for all m and n. For example, the divisor functions and Ramanujan's τ-function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in the literature. In this paper, we provide some further characterizations of specially multiplicative functions.