Two arithmetic functions related to Euler’s and Dedekind’s functions

Krassimir Atanassov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 1, Pages 179–183
DOI: 10.7546/nntdm.2024.30.1.179-183
Full paper (PDF, 225 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., Block 105, 1113 Sofia, Bulgaria

Abstract

Two new arithmetic functions are introduced. In some sense, they are modifications of Euler’s and Dedekind’s functions. Some properties of the new functions are studied.

Keywords

• Arithmetic function
• Dedekind’s function
• Euler’s function

2020 Mathematics Subject Classification

• 11A25

References

1. Atanassov, K. (1987). New integer functions, related to “φ” and “σ” functions, Bulletin of Number Theory and Related Topics, XI (1), 3–26.
2. Atanassov, K. (1987). Some assertions on “φ” and “σ” functions, Bulletin of Number Theory and Related Topics, XI (1), 50–63.
3. Atanassov, K. (2002). Restrictive factor: Definition, properties and problems. Notes on Number Theory and Discrete Mathematics, 8 (4), 117–119.
4. Mitrinović, D., & Popadić, M. (1987). Inequalities in Number Theory. Nis, Univ. of Nis.
5. Nagell, T. (1950). Introduction to Number Theory. John Wiley & Sons, New York.
6. Sándor, J., & Atanassov, K. (2021). Arithmetic Functions. Nova Sciences, New York.
7. Sándor, J., & Crstici, B. (2005). Handbook of Number Theory. Vol. 1. Springer Verlag, Berlin.

Manuscript history

• Received: 27 September 2023
• Revised: 28 December 2023
• Accepted: 23 February 2024
• Online First: 22 March 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).