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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## 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*(*x*^{2})) 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 Jangjian 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

## Cite this paper

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

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

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