**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)**

## Details

### 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.