Inequalities for generalized divisor functions

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 2, Pages 41—48
DOI: 10.7546/nntdm.2021.27.2.41-48
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Authors and affiliations

József Sándor
Department of Mathematics, Babes-Bolyai University
Str. Kogalniceanu 1, 400084 Cluj-Napoca, Romania

Abstract

We offer inequalities to \sigma_a(n) as a function of the real variable a: Monotonicity and convexity properties to this and related functions are proved, too. Extensions and improvements of known results are provided.

Keywords

  • Arithmetic functions
  • Inequalities for arithmetic functions,
  • Monotonicity and convexity of real functions
  • Inequalities for sums
  • Series and integrals

2020 Mathematics Subject Classification

  • 11A25
  • 26D07
  • 26D15
  • 26A51

References

  1. Bullen, P. (2015). Dictionary of Inequalities, second ed., CRC Press, Boca Raton, USA.
  2. Sándor, J., & Tóth, L. (1990). On certain number theoretic inequalities. The Fibonacci Quarterly, 28(3), 255–258.
  3. Sándor, J., & Tóth, L. (1997). On certain arithmetic functions associated with the unitary  divisors of a number. Notes on Number Theory and Discrete Mathematics, 3(1), 1–8.
  4. Sándor, J. (2006). Generalizations of Lehman’s inequality. Soochow Journal of Mathematics, 32(2), 301–309.
  5. Sándor, J. (2009). On the monotonicity of the sequence σk/σk*. Notes on Number Theory and Discrete Mathematics, 15(3), 9–13.
  6. Sándor, J. (2014). On certain inequalities for σ, γ, ψ and related functions. Notes on Number Theory and Discrete Mathematics, 20(2), 52–60.
  7. Sándor, J. & Kovács, L. (2015). On certain upper bounds for the sum of divisors function σ(n). Acta Universitatis Sapientiae, Mathematica, 7(2), 265–277.

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Cite this paper

Sándor, J. (2021). Inequalities for generalized divisor functions. Notes on Number Theory and Discrete Mathematics, 27(2), 41-48, doi: 10.7546/nntdm.2021.27.2.41-48.

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