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Erdős problem 856

Let k≥3k\geq 3 and fk(N)f_k(N) be the maximum of ∑n∈A1n\sum_{n\in A}\frac{1}{n} over all A⊆{1,…,N}A\subseteq\{1,\ldots,N\} containing no kk subsets with the same pairwise least common multiple. Estimate fk(N)f_k(N). The claimed answer: fk(N)=(log⁡N)γk+o(1)f_k(N)=(\log N)^{\gamma_k+o(1)}, where γk\gamma_k is a weighted generalization of the Tang-Zhang sunflower capacity.

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  • AI collaborating with humans

    Erdős AI contributions wiki · 15 Apr, 2026

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    GPT-5.4 Pro
    People
    Przemek Chojecki
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    VibeMathed

    Machine
    GPT-5.4 Pro
    People
    Przemysław Chojecki
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    candidate
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