On a generalization of a function of J. Sándor

V. Siva Rama Prasad and P. Anantha Reddy
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 4, Pages 692–697
DOI: 10.7546/nntdm.2022.28.4.692-697
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Authors and affiliations

V. Siva Rama Prasad
Professor (Retired), Department of Mathematics, Osmania University
Hyderabad, Telangana-500007, India

P. Anantha Reddy
Government Polytechnic
Mahabubnagar, Telangana-509001, India


Using a strictly increasing function \alpha: \left [ 1,\infty \right )\rightarrow \left [ 1,\infty \right ), we define below (see(1.1) and (1.2)) two functions S_{\alpha}:\left [ 1,\infty \right )\rightarrow \mathbb{N} and S_{\alpha}^*:\left [ 1,\infty \right )\rightarrow \mathbb{N}, where \mathbb{N} is the set of all natural numbers. The functions S_{\alpha} and S_{\alpha}^* respectively generalize the functions S and S_{*} introduced and studied by J. Sándor [5] as well as the functions G and G_{*} considered by N. Anitha [1]. In this paper we obtain several properties of S_{\alpha} and S_{\alpha}^* – some of which give the results of Sándor [5] and of Anitha [1] as special cases.


  • Sándor function
  • Riemann integrable
  • Riemann–Stieltjes integrable with respect to a function
  • Prime numbers
  • Asymptotic result

2020 Mathematics Subject Classification

  • Primary: 11A25, 11N37
  • Secondary: 26A42


  1. Anitha, N., (2005). A note on Sandor Type functions. Journal of Inequalities in Pure and Applied Mathematics, 6(4), Article 127.
  2. Apostol, T. M. (1974). Mathematical Analysis (Second Edition). Addison Wesley Publishing Company.
  3. Mincu, G., & Panaitopol, L. (2006). Properties of the Sándor function. Notes on Number Theory and Discrete Mathematics, 12(1), 21–24.
  4. Rohrbach, H., & Weiss, J. (1964). Zum finiten Fall des Bertrandschen Postulats. Journal für die reine und angewandte Mathematik, 214/215, 432–440.
  5. Sándor, J. (2001). On an additive analogue of the function S. Notes on Number Theory and Discrete Mathematics, 7(3), 91–95.

Manuscript history

  • Received: 31 May 2022
  • Revised: 25 October 2022
  • Accepted: 27 October 2022
  • Online First: 28 October 2022

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Cite this paper

Siva Rama Prasad, V., & Anantha Reddy, P. (2022). On a generalization of a function of J. Sándor. Notes on Number Theory and Discrete Mathematics, 28(4), 692-697, DOI: 10.7546/nntdm.2022.28.4.692-697.

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