Skip to Main content Skip to Navigation
Journal articles

On sets of coprime integers in intervals

Abstract : If $\mathcal{A}\subset\mathbb{N}$ is such that it does not contain a subset $S$ consisting of $k$ pairwise coprime integers, then we say that $\mathcal{A}$ has the property $P_k$. Let $\Gamma_k$ denote the family of those subsets of $\mathbb{N}$ which have the property $P_k$. If $F_k(n)=\max_{\mathcal{A}\subset\{1,2,3,\ldots,n\},\mathcal{A}\in\Gamma_k}\vert\mathcal{A}\vert$ and $\Psi_k(n)$ is the number of integers $u\in\{1,2,3,\ldots,n\}$ which are multiples of at least one of the first $k$ primes, it was conjectured that $F_k(n)=\Psi_{k-1}(n)$ for all $k\geq2$. In this paper, we give several partial answers.
Document type :
Journal articles
Complete list of metadata

Cited literature [5 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01108688
Contributor : Ariane Rolland <>
Submitted on : Friday, January 23, 2015 - 11:57:57 AM
Last modification on : Thursday, May 7, 2020 - 10:30:04 AM
Long-term archiving on: : Friday, April 24, 2015 - 10:22:05 AM

File

16Article1.pdf
Explicit agreement for this submission

Identifiers

  • HAL Id : hal-01108688, version 1

Collections

Citation

Paul Erdös, András Sárközy. On sets of coprime integers in intervals. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 1993, 16, pp.1 - 20. ⟨hal-01108688⟩

Share

Metrics

Record views

182

Files downloads

1288