On Vandiver’s arithmetical function – I

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 3, Pages 29—38
DOI: 10.7546/nntdm.2021.27.3.29-38
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Authors and affiliations

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

Abstract

We study certain properties of Vandiver’s arithmetic function V(n) = \prod_{d|n} (d+1).

Keywords

  • Arithmetic function
  • Inequalities
  • Generalized perfect numbers

2020 Mathematics Subject Classification

  • 11A25
  • 11A41
  • 11N37
  • 26D15

References

  1. Beckenbach, E. F., & Bellman, R. (1961). Inequalities, Springer-Verlag.
  2. Lehmer, D. H. (1974). Harry Schultz Vandiver. Bulletin of the American
    Mathematical Society, 80, 817–818.
  3. Sándor, J. (2001). On multiplicatively perfect numbers. Journal of Inequalities in Pure and  Applied Mathematics, 2(1), Article No. 3, 6 pages.
  4. Sándor, J., Mitrinovic, D. S., & Crstici, B. (2006). Handbook of Number Theory. Vol. 1. Springer.
  5. Sándor, J., & Toth, L.(2008).On multiplicatively σ-perfect numbers. Octogon Mathematical  Magazine, 16(2), 906–908.
  6. Vandiver, H. S. (1904). Problem 116. American Mathematical Monthly, 11, 38–39.

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Cite this paper

Sándor, J. (2021). Inequalities for generalized divisor functions. Notes on Number Theory and Discrete Mathematics, 27(3), 29-38, doi: 10.7546/nntdm.2021.27.3.29-38.

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