Basic properties of weakly multiplicative functions

Pentti Haukkanen
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 8, 2002, Number 2, Pages 70–74
Full paper (PDF, 1980 Kb)

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Authors and affiliations

Pentti Haukkanen
Department of Mathematics, Statistics and Philosophy
FIN-33014 University of Tampere, Finland

Abstract

An arithmetical function f is said to be weakly multiplicative if f is not identically zero and f(np) = f(n)f(p) for all positive integers n and primes p with (n, p) = 1. Every multiplicative function is a weakly multiplicative function but the converse is not true. In this note we study basic properties of weakly multiplicative functions with respect to the Dirichlet convolution.

AMS Classification

• 11A25

References

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