Mladen Vassilev-Missana and Peter Vassilev

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

Volume 17, 2011, Number 2, Page 31—36

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## Details

### Authors and affiliations

Mladen Vassilev-Missana

*5 V. Hugo Str., Sofia–1124, Bulgaria*

Peter Vassilev

*Institute of Biophysics and Biomedical Engineering*

### Abstract

The paper is a continuation of [1] and [2]. The considerations are over the class of multiplicative functions with strictly positive values and more precisely, over the pairs (*f*, *g*) of such functions, which have a special property, called in the paper property **S**. For every two such pairs (*f*_{1}, *g*) and (*f*_{2}, *g*), with different *f*_{1} and *f*_{2}, a sufficient condition for the coincidence of the maximum (respectively of the minimum) of the numbers *f*_{1}(*d*)*g*(*n*/*d*) and *f*_{2}(*d*)*g*(*n*/*d*), where d runs over all proper divisors of an arbitrary composite number *n* > 1, is given. Some applications of the results are made for several classical multiplicative functions like Euler’s totient function *φ*, Dedekind’s function *ψ*, the sum of all divisors of m, i.e. *σ(m)*, the number of all divisors of m, i.e. *τ(m)*, and 2* ^{ω(m)}*, where

*ω(m)*is the number of all prime divisors of

*m*.

### Keywords

- Multiplicative functions
- Divisors
- Proper divisors
- Prime numbers
- Composite number

### AMS Classification

- 11A25

### References

- Vassilev-Missana, V. Some Results on Multiplicative Functions. Notes on Number Theory and Discrete Mathematics, Vol. 16, 2010, No. 4, 29-40
- Vassilev-Missana, V., P. Vassilev. New Results on Some Multiplicative Functions. Notes on Number Theory and Discrete Mathematics, Vol. 17, 2011, No. 2, 18-30
- Polya, G., G. Szegő Problems and Theorems in Analysis II, Springer-Verlag, Berlin Heidelberg, 1998, 120-125
- Sándor, J., B. Crstici. Handbook of Number Theory II, Kluwer Academic Publishers, Dortrecht/Boston/London, 2004

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## Cite this paper

APAVassilev-Missana, M., & Vassilev, P. (2011). On multiplicative functions with strictly positive values. Notes on Number Theory and Discrete Mathematics, 17(2), 31-36.

ChicagoVassilev-Missana, Mladen, and Peter Vassilev. “On Multiplicative Functions with Strictly Positive Values.” Notes on Number Theory and Discrete Mathematics 17, no. 2 (2011): 31-36.

MLAVassilev-Missana, Mladen, and Peter Vassilev. “On Multiplicative Functions with Strictly Positive Values.” Notes on Number Theory and Discrete Mathematics 17.2 (2011): 31-36. Print.