On certain rational perfect numbers

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 2, Pages 281–285
DOI: 10.7546/nntdm.2022.28.2.281-285
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Authors and affiliations

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

Abstract

We study equations of type \sigma(n) = \dfrac{k+1}{k} \cdot n+a, where a\in \{0, 1, 2, 3\}, where k and n are positive integers, while \sigma(n) denotes the sum of divisors of n.

Keywords

  • Sum of divisors
  • Perfect numbers

2020 Mathematics Subject Classification

  • 11A25

References

  1. Sándor, J. (1989). On the composition of some arithmetic functions. Studia Universitatis Babeș-Bolyai, Mathematica, 34(1), 7–14.
  2. Sándor, J. (2001). On even perfect and superperfect numbers. Notes on Number Theory and Discrete Mathematics, 7(1), 4–5.
  3. Sándor, J. (2006). An extension of k-perfect numbers. Research Group in Mathematical Inequalities and Applications, 9(4), Article 4.
  4. Sándor, J. (2008). On kp-perfect numbers. Matlap, 12(8), 297–298 (in Hungarian).
  5. Sándor, J., & Atanassov, K. T. (2021). Arithmetic Functions. Nova Science Publishers, New York.
  6. Sándor, J., Mitrinović, D. S., & Crstici, B. (2006). Handbook of Number Theory I. Springer, Dordrecht.

Manuscript history

  • Received: 12 March 2022
  • Revised: 11 May 2022
  • Accepted: 11 May 2022
  • Online First: 12 May 2022

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Cite this paper

Sándor, J. (2022). On certain rational perfect numbers. Notes on Number Theory and Discrete Mathematics, 28(2), 281-285, DOI: 10.7546/nntdm.2022.28.2.281-285.

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