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)
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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
- Dimitrov, S. (2023). Lower bounds on expressions dependent on functions φ(n), ψ(n) and σ(n). Notes on Number Theory and Discrete Mathematics, 29(4), 713–716.
- 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.
- Dimitrov, S. (2024). Inequalities involving arithmetic functions. Lithuanian Mathematical Journal. Available online at: https://doi.org/10.1007/s10986-024-09655-x.
- Sandor, J. (1996). On certain inequalities involving Dedekind’s arithmetical functions. Notes on Number Theory and Discrete Mathematics, 2(1), 1–4.
- 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.
- Sándor, J. (2024). On certain inequalities for the prime counting function – Part III. Notes on Number Theory and Discrete Mathematics, 29(3), 454–461.
- Sándor, J., & Atanassov, K. T. (2021). Arithmetic Functions. Nova Science Publ., New York.
- 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).
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- 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.
- 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.
- Sándor, J. (2024). On certain inequalities for the prime counting function – Part III. Notes on Number Theory and Discrete Mathematics, 29(3), 454–461.
- Dimitrov, S. (2023). Lower bounds on expressions dependent on functions φ(n), ψ(n) and σ(n). Notes on Number Theory and Discrete Mathematics, 29(4), 713–716.
- Sandor, J. (1996). On certain inequalities involving Dedekind’s arithmetical functions. Notes on Number Theory and Discrete Mathematics, 2(1), 1–4.
Cite this paper
Sándor, J., & Atanassov, K. (2024). Some new arithmetic functions. Notes on Number Theory and Discrete Mathematics, 30(4), 851-856, DOI: 10.7546/nntdm.2024.30.4.851-856.
