On the extensions of two arithmetical functions and some of their properties

Mladen Vassilev-Missana and Peter Mladenov Vassilev
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 1, Pages 127–132
DOI: 10.7546/nntdm.2025.31.1.127-132
Full paper (PDF, 246 Kb)

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Authors and affiliations

Mladen Vassilev-Missana
5 Victor Hugo Str., 1124 Sofia, Bulgaria

Peter Mladenov Vassilev
Bioinformatics and Mathematical Modelling Department, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
Acad. G. Bonchev Str., Bl. 105, 1113 Sofia, Bulgaria

Abstract

In the paper, an extension of the well-known Jordan’s totient function and generalized Dedekind psi-function are proposed and some properties of theirs are studied.

Keywords

• Arithmetical functions
• Multiplicative functions
• Jordan’s totient function
• Dedekind psi-function
• Primes

2020 Mathematics Subject Classification

• 11A25

References

1. Dickson, L. (1966). History of the Theory of Numbers. Vol. I: Divisibility and Primality. Chelsea Publishing Co., New York.
2. Sierpiński, W. (1964). Elementary Theory of Numbers. Panstwowe Wydawnictwo Naukowe, Warszawa.
3. Burton, D. M. (2007). Elementary Number Theory (6th ed.). McGraw Hill Higher Education, New York.
4. Jahnke, E., Emde, F., & Lösch, F. (1960). Tables of Higher Functions. Teubner, Stuttgart.

Manuscript history

• Received: 9 December 2024
• Revised: 10 April 2025
• Accepted: 18 April 2025
• Online First: 24 April 2025

Copyright information

Ⓒ 2025 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).