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 | 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
- C. Adiga and K. Taekyun. On a generalization of the Sándor function. Proc. of the Jangjeon Math. Soc No. 2 (2002), 121-124.
- H. Rohrbach and J Weiss. Zum finiten Fall des Bertrandschen Postulats. J. Reinen Angew. Math. 214/215 (1964) 432-440.
- J. Sándor, An additive analogue of the function S. Notes on Number Theory and Discrete Mathematics 7, no. 2 (2001), 91-95.
Related papers
- Sándor, J. (2001). An additive analogue of the function S. Notes on Number Theory and Discrete Mathematics, 7(2), 91-95.
- 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.
Cite this paper
Mincu, J., & Panaitopol, L. (2006). Properties of the Sándor function. Notes on Number Theory and Discrete Mathematics, 12(1), 21-24.