On a conjecture of Erdős concerning primitive sequences

2011/04/19 by Bakir Farhi, Farhi, Bakir
Mathematics · #11Bxx #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1104.3724

openalex publication_date 2011/04/19 · openalex created_date 2021/02/15 · openalex updated_date 2026/07/28

Abstract

In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erdős, for those series, is false.

Related

• Results and conjectures related to a conjecture of Erdős concerning primitive sequences
• Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond
• Erdős inequality for primitive sets
• The convergence of an alternating series of Erdős, assuming the Hardy--Littlewood prime tuples conjecture
• Primitive sets with large counting functions