Stoyan Dimitrov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 3, Pages 547–556
DOI: 10.7546/nntdm.2024.30.3.547-556
Full paper (PDF, 195 Kb)
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Authors and affiliations
Stoyan Dimitrov 
Faculty of Applied Mathematics and Informatics, Technical University of Sofia
8 St. Kliment Ohridski Blvd., Sofia 1756, Bulgaria
and
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
In this paper we establish lower bounds on several expressions dependent on functions 
, 
and 
.
Keywords
- Arithmetic functions , and
- Lower bounds
2020 Mathematics Subject Classification
- 11A25
References
- 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.
- Sándor, J., Mitrinović, D. S., & Crstici, B. (2006). Handbook of Number Theory I. Springer.
- Sándor, J., & Tóth, L. (1990). On certain number-theoretic inequalities. The Fibonacci Quarterly, 28(3), 255–258.
Manuscript history
- Received: 18 November 2023
- Accepted: 1 October 2024
- Online First: 3 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
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, DOI: 10.7546/nntdm.2024.30.3.547-556.
