Some new arithmetic functions

József Sándor and Krassimir Atanassov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 4, Pages 851–856
DOI: 10.7546/nntdm.2024.30.4.851-856
Full paper (PDF, 164 Kb)

Details

Authors and affiliations

József Sándor
Department of Mathematics, Babeș-Bolyai University
Str. Kogalniceanu 1, 400084 Cluj-Napoca, Romania

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

Abstract

We introduce and study some new arithmetic functions, connected with the classical functions (Euler’s totient), (Dedekind’s function) and (sum of divisors function).

Keywords

• Arithmetic functions
• Inequalities for arithmetic functions

2020 Mathematics Subject Classification

• 11A25
• 26D15

References

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2. Dimitrov, S. (2024). Lower bounds on expressions dependent on functions φ(n), ψ(n) and σ(n), II. Notes on Number Theory and Discrete Mathematics, 30(3), 547–556.
3. Dimitrov, S. (2024). Inequalities involving arithmetic functions. Lithuanian Mathematical Journal. Available online at: https://doi.org/10.1007/s10986-024-09655-x.
4. Sandor, J. (1996). On certain inequalities involving Dedekind’s arithmetical functions. Notes on Number Theory and Discrete Mathematics, 2(1), 1–4.
5. Sandor, J. (2024). On certain inequalities for φ(n), ψ(n), σ(n) and related functions, II. Notes on Number Theory and Discrete Mathematics, 30(3), 575–579.
6. Sándor, J. (2024). On certain inequalities for the prime counting function – Part III. Notes on Number Theory and Discrete Mathematics, 29(3), 454–461.
7. Sándor, J., & Atanassov, K. T. (2021). Arithmetic Functions. Nova Science Publ., New York.
8. Sándor, J., Mitrinović, D. S., & Crstici, B. (2005). Handbook of Number Theory, Vol. 1. Springer Verlag, New York.

Manuscript history

• Received: 7 February 2024
• Revised: 8 December 2024
• Accepted: 11 December 2024
• Online First: 11 December 2024

Copyright information

Ⓒ 2024 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).