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Claim. Yes: the complement of the odd squarefree numbers is a largest $A\subseteq\{1,\ldots,n\}$ in which no product of two members is squarefree, as Erdős and Sárközy guessed; it attains the maximum but is not always the only set that does.

Argument. The squarefree graph has the squarefree integers up to $n$ as vertices, two of them adjacent when their product is squarefree, that is, when they are coprime; an admissible set is an independent set together with non-squarefree numbers, which are isolated. Theorem 2 of the paper partitions the vertices into cliques each containing exactly one even vertex, so no independent set is larger than the set of even vertices (Theorem 1), and the clique cover number, the independence number and the Lovász number all equal the count of even squarefree numbers up to $n$. The proof is independent of Chvátal's theorem and of Weisenberg's reduction, which the paper records in its Subsection 1.1.

Source. Boris Alexeev, Dustin G. Mixon and Will Sawin, The independence and clique cover numbers of the squarefree graph, arXiv:2507.01928, v1 of 2 July 2025 and v2 of 3 July 2025 (minor changes), CC BY 4.0; no journal version is recorded. The library's source card digests the paper; its theorems are not transcribed as result pages.

Acceptance. Reviewed: the site's curator, Thomas Bloom, marks Problem 844 proved and credits the paper as an independent alternative proof. The preprint is not refereed, and this corpus has not reviewed it.