On a modification of Set(n)

Krassimir T. Atanassov and József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 4, Pages 813–819
DOI: 10.7546/nntdm.2023.29.4.813-819
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Authors and affiliations

Krassimir T. Atanassov
Dept. of Bioinformatics and Mathematical Modelling
Institute of Biophysics and Biomedical Engineering,
Bulgarian Academy of Sciences
105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria

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

Abstract

A modification of the set \underline{\rm Set}(n) for a fixed natural number n is introduced in the form: \underline{\rm Set}(n, f), where f is an arithmetic function. The sets \underline{\rm Set}(n,\varphi), \underline{\rm Set}(n,\psi), \underline{\rm Set}(n,\sigma) are discussed, where \varphi, \psi and \sigma are Euler’s function, Dedekind’s function and the sum of the positive divisors of n, respectively.

Keywords

  • Arithmetic function
  • Functions \varphi, \psi and \sigma
  • \underline{\rm Set}(n)

2020 Mathematics Subject Classification

  • 11A25

References

  1. Atanassov, K. (2020). Objects generated by an arbitrary natural number. Notes on Number Theory and Discrete Mathematics, 26(4), 57–62.
  2. Sándor, J., & Crstici, B. (2005) Handbook of Number Theory. II. Springer Verlag, Berlin.

Manuscript history

  • Received: 13 July 2023
  • Revised: 30 October 2023
  • Accepted: 13 November 2023
  • Online First: 2 December 2023

Copyright information

Ⓒ 2023 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).

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Cite this paper

Atanassov, K., & Sándor, J. (2023). On a modification of Set(n). Notes on Number Theory and Discrete Mathematics, 29(4), 813-819, DOI: 10.7546/nntdm.2023.29.4.813-819.

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