Inequalities between some arithmetic functions, II

Krassimir Atanassov, József Sándor and Mladen Vassilev-Missana
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 4, Pages 839–845
DOI: 10.7546/nntdm.2025.31.4.839-845
Full paper (PDF, 212 Kb)

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Authors and affiliations

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

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

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

Abstract

As a continuation of Part I (see [1]), we offer new inequalities for classical arithmetic functions such as the Euler’s totient function, the Dedekind’s psi function, the sum of the positive divisors function, the number of divisors function, extended Jordan’s totient function, generalized Dedekind’s psi function.

Keywords

• Arithmetic functions
• Inequalities

2020 Mathematics Subject Classification

• 11A25
• 26D99

References

1. Sándor, J., & Atanassov, K. (2025). Inequalities with some arithmetic functions. Mathematics, 13(8), Article ID 1253.
2. Sándor, J., Mitrinović, D. S., & Crstici, B. (2006). Handbook of Number Theory, Volume 1. Springer, New York.
3. Vassilev-Missana, M., & Vassilev, P. M. (2025). On the extensions of two arithmetical functions and some of their properties. Notes on Number Theory and Discrete Mathematics, 31(1), 127–132.

Manuscript history

• Received: 13 August 2025
• Revised: 8 November 2025
• Accepted: 11 November 2025
• Online First: 12 November 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).