József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 3, Pages 575–579
DOI: 10.7546/nntdm.2024.30.3.575-579
Full paper (PDF, 173 Kb)
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Authors and affiliations
József Sándor 
Department of Mathematics, Babeș-Bolyai University
Str. Kogalniceanu 1, 400084 Cluj-Napoca, Romania
Abstract
We offer new proofs and refinements of two inequalities from paper [2]. The unitary functions variants are also considered.
Keywords
- Arithmetic functions
- Inequalities
2020 Mathematics Subject Classification
- 11A25
References
- Atanassov, K. (2013). Note on φ, ψ and σ-functions. Part 6. Notes on Number Theory and Discrete Mathematics, 19(1), 22–24.
- 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.
- Sándor, J. (2014). On certain inequalities for φ, ψ, σ and related functions. Notes on Number Theory and Discrete Mathematics, 20(2), 52–60.
- Sándor, J., Mitrinović, D. S., & Crstici, B. (2006). Handbook of Number Theory I. Springer.
Manuscript history
- Received: 11 December 2023
- Accepted: 2 October 2024
- Online First: 6 October 2024
Copyright information
Ⓒ 2024 by the Author.
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).
Related papers
- Atanassov, K. (2011). Note on φ, ψ and σ-functions. Part 3. Notes on Number Theory and Discrete Mathematics, 17(3), 13–14.
- Atanassov, K. (2013). Note on φ, ψ and σ-functions. Part 6. Notes on Number Theory and Discrete Mathematics, 19(1), 22–24.
- 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.
- Sándor, J. (2014). On certain inequalities for φ, ψ, σ and related functions. Notes on Number Theory and Discrete Mathematics, 20(2), 52–60.
- Sándor, J., & Atanassov, K. (2019). Inequalities between the arithmetic functions φ, ψ and σ. Part 2. Notes on Number Theory and Discrete Mathematics, 25(2), 30–35.
Cite this paper
Sándor, J. (2024). On certain inequalities for φ, ψ, σ, and related functions, II. Notes on Number Theory and Discrete Mathematics, 30(3), 575-579, DOI: 10.7546/nntdm.2024.30.3.575-579.
