Nadir Rezzoug, Ilias Laib and Guenda Kenza

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367-8275

Volume 26, 2020, Number 4, Pages 68–73

DOI: 10.7546/nntdm.2020.26.4.68-73

**Full paper (PDF, 156 Kb)**

## Details

### Authors and affiliations

Nadir Rezzoug

* Laboratory of Analysis and Control of Partial Differential Equations
Faculty of Exact Sciences, Djillali Liabes University
Sidi Bel Abbes, Algeria
*

Ilias Laib

*ENSTP, Garidi Kouba, 16051, Algiers, Algeria*

and Laboratory of Equations with Partial Non-Linear Derivatives

ENS Vieux Kouba, Algiers, Algeria

and Laboratory of Equations with Partial Non-Linear Derivatives

ENS Vieux Kouba, Algiers, Algeria

Guenda Kenza

*Faculty of Mathematics, University of Sciences and Technology Houari Boumédiène,*

Algiers, Algeria

Algiers, Algeria

### Abstract

For large enough, there exists a primitive sequence , such that

where denotes the set of prime numbers.

### Keywords

- Primitive sequences
- Erdős conjecture
- Prime numbers

### 2010 Mathematics Subject Classification

- 11Bxx

### References

- Dusart., P. (1998). Autour de la fonction qui compte le nombre de nombres premiers, thèse de doctorat, université de Limoges, 17-1998.
- Erdős, P. (1935). Note on sequences of integers no one of which is divisible by any other, J.Lond. Math. Soc, 10, 126–128.
- Erdős, P., & Zhang, Z. (1993). Upper bound of for primitive sequences, Math. Soc, 117, 891–895.
- Farhi, B. (2017). Results and conjectures related to a conjecture of Erdős concerning primitive sequences, arXiv: 1709.08708v2 [math.NT] 25 Sep 2017.
- Laib, I., Derbal, A. & Mechik, R. (2019). Somme translatée sur des suites primitives et la conjecture d’Erdős. C. R. Acad. Sci. Paris, Ser. I, 357, 413–417.
- Massias, J.-P., & Robin, G. (1996). Bornes effectives pour certaines fonctions concernant les nombres premiers, J. Theori. Nombres Bordeaux, 8, 215–242.
- Robbins, H. (1955). A remark on Stirling’s formula, Amer. Math. Monthly, 62, 26–29.
- Rosser, J. B., & Schoenfeld, L. (1962). Approximates formulas for some functions of prime numbers, Illinois Journal Math, 6, 64–94.

## Related papers

- Laib, I. (2021). Note on translated sum on primitive sequences.
*Notes on Number Theory and Discrete Mathematics*, 27(3), 39-43.

## Cite this paper

Rezzoug, N., Laib, I. & Kenza, G. (2020). On a translated sum over primitive sequences related to a conjecture of Erdős. *Notes on Number Theory and Discrete Mathematics*, 26 (4), 68-73, DOI: 10.7546/nntdm.2020.26.4.68-73.