Note on translated sum on primitive sequences

Ilias Laib
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 3, Pages 39—43
DOI: 10.7546/nntdm.2021.27.3.39-43
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Authors and affiliations

Ilias Laib
ENSTP, Garidi Kouba, 16051, Algiers,
and Laboratory of Equations with Partial Non-Linear Derivatives,
ENS Vieux Kouba, Algiers, Algeria

Abstract

In this note, we construct a new set \boldsymbol{S} of primitive sets such that for any real number x\geq 60 we get:

    \begin{equation*} \sum\limits_{a\in \mathcal{A}}\frac{1}{a(\log a+x)}>\sum\limits_{p\in \mathcal{P}}\frac{1}{p(\log p+x)},\text{ }\mathcal{A\in }{\boldsymbol{S}}, \end{equation*}

where \mathcal{P} denotes the set of prime numbers.

Keywords

  • Primitive sequences
  • Erdős’s conjecture
  • Prime numbers
    Integer sequences

2020 Mathematics Subject Classification

  • 11B05
  • 11Y55
  • 11L20

References

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Related papers

  1. Rezzoug, N., Laib, I., & Guenda, K. (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.

Cite this paper

Laib, I. (2021). Note on translated sum on primitive sequences. Notes on Number Theory and Discrete Mathematics, 27(3), 39-43, doi: 10.7546/nntdm.2021.27.3.39-43.

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