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Article Dans Une Revue Hardy-Ramanujan Journal Année : 1993

On sets of coprime integers in intervals

Résumé

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.
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Dates et versions

hal-01108688 , version 1 (23-01-2015)

Identifiants

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Paul Erdös, András Sárközy. On sets of coprime integers in intervals. Hardy-Ramanujan Journal, 1993, Volume 16 - 1993, pp.1 - 20. ⟨10.46298/hrj.1993.126⟩. ⟨hal-01108688⟩
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