Problem detail · source-aware
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Let $k\geq 3$ and $f_k(N)$ be the maximum of $\sum_{n\in A}\frac{1}{n}$ over all $A\subseteq\{1,\ldots,N\}$ containing no $k$ subsets with the same pairwise least common multiple. Estimate $f_k(N)$. The claimed answer: $f_k(N)=(\log N)^{\gamma_k+o(1)}$, where $\gamma_k$ is a weighted generalization of the Tang-Zhang sunflower capacity.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
A weighted version of the Tang-Zhang sunflower-capacity argument giving the exact logarithmic exponent was developed with GPT-5.4 Pro, using a mass-transport idea from the forum's discussion of problem #1196.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
An AI screening found no issues and no prior literature with the result; the site's owner unpacked and restated the main claim without checking details, a Lean formalization attempt hit missing mathlib prerequisites, and the problem is still listed open.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Identifies the exponent as a variational sunflower-capacity constant, sharpening the Tang-Zhang bounds; the value of that constant itself remains open, as does site acceptance
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.