József Sándor and Krassimir Atanassov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 2, Pages 30–35
DOI: 10.7546/nntdm.2019.25.2.30-35
Full paper (PDF, 161 Kb)
Details
Authors and affiliations
József Sándor 
Department of Mathematics, Babeș–Bolyai University
Str. Kogalniceanu 1, 400084 Cluj-Napoca, Romania
Krassimir T. 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
and
Intelligent Systems Laboratory, Prof. Asen Zlatarov University
Bourgas-8000, Bulgaria
Abstract
We prove inequalities related to 
or 
and related powers, where 
and 
denote the Euler, resp. Dedekind arithmetic functions. More general theorem for the arithmetical functions 
, 
and 
is formulated and proved.
Keywords
- Arithmetic function
- Inequality
2010 Mathematics Subject Classification
- 11A25
- 26D15.
References
- Atanassov, K. (2011). Note on φ, ψ and σ-functions. Part 3. Notes on Number Theory and Discrete Mathematics, 17 (3), 13–14.
- Kannan, V. & Srikanth, R. (2013). Note on φ and ψ functions. Notes on Number Theory and Discrete Mathematics, 19 (1), 19–21.
- Mitrinovich, D. (1970). Analytic Inequalities. Springer Verlag, Berlin.
- Atanassov, K., & Sándor, J. (2019). Inequalities between the arithmetic functions φ, ψ and σ. Part 1. Notes on Number Theory and Discrete Mathematics, 25 (1), 50–53.
- Sándor, J. (2018). Theory of means and their inequalities (online book)
- Sándor, J. (2014). On certain inequalities for σ, φ, ψ and related functions. Notes on Number Theory and Discrete Mathematics, 20 (2), 52–60.
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.
- Kannan, V. & Srikanth, R. (2013). Note on φ and ψ functions. Notes on Number Theory and Discrete Mathematics, 19 (1), 19–21.
- Atanassov, K., & Sándor, J. (2019). Inequalities between the arithmetic functions φ, ψ and σ. Part 1. Notes on Number Theory and Discrete Mathematics, 25 (1), 50–53.
- Sándor, J. (2014). On certain inequalities for σ, φ, ψ and related functions. Notes on Number Theory and Discrete Mathematics, 20 (2), 52–60.
- 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.
Cite this paper
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, DOI: 10.7546/nntdm.2019.25.2.30-35.
