On certain rational perfect numbers, II

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 3, Pages 525–532
DOI: 10.7546/nntdm.2022.28.3.525-532
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Authors and affiliations

József Sándor
Department of Mathematics, Babeș-Bolyai University
Cluj-Napoca, Romania

Abstract

We continue the study from [1], by studying equations of type \psi(n) = \dfrac{k+1}{k} \cdot \ n+a, a\in \{0, 1, 2, 3\}, and \varphi(n) = \dfrac{k-1}{k} \cdot \ n-a, a\in \{0, 1, 2, 3\} for k > 1, where \psi(n) and \varphi(n) denote the Dedekind, respectively Euler’s, arithmetical functions.

Keywords

  • Arithmetical functions
  • Dedekind’s function
  • Euler’s totient

2020 Mathematics Subject Classification

  • 11A25

References

  1. Sándor, J. (2022). On certain rational perfect numbers. Notes on Number Theory and Discrete Mathematics, 28(2), 281–285.
  2. Sándor, J., & Atanassov, K. T. (2021). Arithmetic Functions. Nova Science Publishers, New York.
  3. Sándor, J., Mitrinović, D. S., & Crstici, B. (2006). Handbook of Number Theory, I. Springer, Dordrecht.

Manuscript history

  • Received: 4 May 2022
  • Revised: 31 July 2022
  • Accepted: 6 August 2022
  • Online First: 10 August 2022

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Cite this paper

Sándor, J. (2022). On certain rational perfect numbers, II. Notes on Number Theory and Discrete Mathematics, 28(3), 525-532, DOI: 10.7546/nntdm.2022.28.3.525-532.

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