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
Full paper (PDF, 127 Kb)

Details

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 | x ≤ m!}. 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 Jangjeon 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.