Pentti Haukkanen

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 8, 2002, Number 2, Pages 70—74

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## Details

### 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

- T. M. Apostol. Introduction to Analytic Number Theory. UTM. New York: Springer-Verlag, 1976.
- I. Katai & M. V. Subbarao. “Quasi-additive and quasi-multiplicative functions with regularity properties.” Publ. Math. 56 (2000): 43-52.
- P. J. McCarthy. Introduction to Arithmetical Functions. Universitext. New York: Springer-Verlag, 1986.
- R. Sivaramakrishnan. Classical Theory of Arithmetic Functions. Monographs and Textbooks in Pure and Applied Mathematics, Vol. 126. New York: Marcel Dekker, Inc., 1989.

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## Cite this paper

APAHaukkanen, P. (2002). Basic properties of weakly multiplicative functions. Notes on Number Theory and Discrete Mathematics, 8(2), 70-74.

ChicagoHaukkanen, Pentti. “Basic Properties of Weakly Multiplicative Functions.” Notes on Number Theory and Discrete Mathematics 8, no. 2 (2002): 70-74.

MLAHaukkanen, Pentti. “Basic Properties of Weakly Multiplicative Functions.” Notes on Number Theory and Discrete Mathematics 8.2 (2002): 70-74. Print.