On certain equations and inequalities involving the arithmetical functions φ(n) and d(n)

József Sándor and Saunak Bhattacharjee
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 2, Pages 376–379
DOI: 10.7546/nntdm.2022.28.2.376-379
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Authors and affiliations

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

Saunak Bhattacharjee
Indian Institute of Science Education and Research
Tirupati, India

Abstract

By using the results and methods of [1], we will study the equation \varphi(n) + d(n) = \frac{n}{2} and the related inequalities. The equation \varphi(n) + d^2(n)=2n will be solved, too.

Keywords

  • Arithmetic functions
  • Inequalities

2020 Mathematics Subject Classification

  • 11A25

References

  1. Sándor, J. (2020). On the equation \varphi(n) + d(n) = n and related inequalities. Notes on Number Theory and Discrete Mathematics, 26(3), 1–4.
  2. Sándor, J., & Atanassov, K. T. (2021). Arithmetic Functions. Nova Science Publishers, New York.
  3. Sándor, J., & Kovács, L. (2009). An inequality for the number of divisors. Octogon Mathematical Magazine, 17(2), 746–749.
  4. Sándor, J., Mitrinović, D. S., & Crstici, B. (2005). Handbook of Number Theory I. Springer.

Manuscript history

  • Received: 10 January 2022
  • Revised: 27 May 2022
  • Accepted: 9 June 2022
  • Online First: 14 June 2022

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Cite this paper

Sándor, J. & Bhattacharjee, S. (2022). On certain equations and inequalities involving the arithmetical functions φ(n) and d(n). Notes on Number Theory and Discrete Mathematics, 28(2), 376-379, DOI: 10.7546/nntdm.2022.28.2.376-379.

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