Year: 2026
Type: preprint
Abstract: Let $F(n)$ be the largest size of a set $A\subseteq[1,n]$ such that $a\nmid bc$ whenever $a,b,c\in A$ and $a\notin\{b,c\}$, with $b$ and $c$ allowed to coincide. We prove \[ F(n)=π(n)+\left(\frac{27}{2}+o(1)\right)\frac{n^{2/3}}{(\log n)^2}. \] This determines the second-order constant conjectured by Erdős; the upper bound keeps the leading constants in his multiplicative basis, while the lower bound packs scale-separated prime triples by proper edge-colourings.
Source: arXiv (Cornell University)
Author: Chojecki, Przemek
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169759698
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