Properties of the Sándor function

Gabriel Mincu and Laurențiu Panaitopol
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 12, 2006, Number 1, Pages 21—24
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Authors and affiliations

Gabriel Mincu
Faculty of Mathematics
Str. Academiei 14, RO-010014 Bucharest, Romania

Laurențiu Panaitopol
Faculty of Mathematics
Str. Academiei 14, RO-010014 Bucharest, Romania

Abstract

For x > 0 one define the function S(x) = min{m ∈ ℕ | xm!}. We prove that for x > √13! the interval (S(x), S(x2)) contains at least a prime number and that for real x, y > 0 the inequality S(x) + S(y) ≥ S(xy) holds true. We also study the convergence of a couple of number series involving S(x).

Keywords

  • Sándor function
  • Prime numbers
  • Inequalities
  • Series

AMS Classification

  • 11A25
  • 11A41

References

  1. C. Adiga and K. Taekyun. On a generalization of the Sándor function. Proc. of the Jangjian Math. Soc No. 2 (2002), 121-124.
  2. H. Rohrbach and J Weiss. Zum finiten Fall des Bertrandschen Postulats. J. Reinen Angew. Math. 214/215 (1964) 432-440.
  3. J. Sándor, An additive analogue of the function S. Notes on Number Theory and Discrete Mathematics 7, no. 2 (2001), 91-95.

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Cite this paper

APA

Mincu, J., & Panaitopol, L. (2006). Properties of the Sándor function. Notes on Number Theory and Discrete Mathematics, 12(1), 21-24.

Chicago

Mincu, Gabriel, and Laurențiu Panaitopol. “Properties of the Sándor Function.” Notes on Number Theory and Discrete Mathematics 12, no. 1 (2006): 21-24.

MLA

Mincu, Gabriel, and Laurențiu Panaitopol. “Properties of the Sándor Function.” Notes on Number Theory and Discrete Mathematics 12.1 (2006): 21-24. Print.

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