On certain arithmetical functions connected with the prime factorization of an integer

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 32, 2026, Number 1, Pages 88–95
DOI: 10.7546/nntdm.2026.32.1.88-95
Full paper (PDF, 250 Kb)

Details

Authors and affiliations

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

Abstract

If 1< n = \displaystyle\prod_{i=1}^r p_i^{a_i} is the prime factorization of integer n, we study the arithmetical functions

    \[M(n) = \displaystyle\prod_{i=1}^r a_i^{p_i}, \quad F(n) = \displaystyle\prod_{i=1}^r p_i^{1/a_i},\quad G(n) = \displaystyle\prod_{i=1}^r a_i^{1/p_i}.\]

Keywords

  • Arithmetical functions
  • Inequalities for arithmetical functions
  • Prime numbers
  • Asymptotic results
  • Inequalities for real numbers

2020 Mathematics Subject Classification

  • 11A25
  • 11A51
  • 11N37
  • 26D07

References

  1. Atanassov, K. (1996). Irrational factor: Definition, properties and problems. Notes on Number Theory and Discrete Mathematics, 2(3), 42–44.
  2. Atanassov, K. (2002). Converse factor: Definition, properties and problems. Notes on Number Theory and Discrete Mathematics, 8(1), 37–38.
  3. Dickson, L. E. (1919). History of the Theory of Numbers, Vol. I. Carnegie Institution, Washington.
  4. Meissner, O. (1907). Math. Naturw. Blatter, 4, 85–86.
  5. Sándor, J. (2005). On Meissner’s arithmetic function. Octogon Mathematical Magazine, 13(1), 192–194.
  6. Sándor, J., & Atanassov, K. (2023). On certain arithmetical functions of exponents in the factorization of integers. Notes on Number Theory and Discrete Mathematics, 29(2), 378–388.
  7. Sándor, J., & Cristici, B. (2005). Handbook of Number Theory, II. Springer.
  8. Sándor, J., Mitrinović, D. S., & Cristici, B. (2006). Handbook of Number Theory, I. Springer.

Manuscript history

  • Received: 19 September 2025
  • Revised: 22 February 2026
  • Accepted: 23 February 2026
  • Online First: 23 February 2026

Copyright information

Ⓒ 2026 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Related papers

Cite this paper

Sándor, J. (2026). On certain arithmetical functions connected with the prime factorization of an integer. Notes on Number Theory and Discrete Mathematics, 32(1), 88-95, DOI: 10.7546/nntdm.2026.32.1.88-95.

Comments are closed.