If each integer has at most $r$ representations $m = pa$ with $p$ prime and $a \in A \subseteq [1, N]$, what is the best upper bound for $\sum_{a \in A} 1/a$? The candidate proof gives the matching order $\Theta_r(\log N / \log\log N)$.

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1True ↔2  ∀ (r : ℕ),3    2 ≤ r →4      ∃ c,5        0 < c ∧6          Filter.Tendsto (fun N => Erdos538.maxMass r N * Real.log (Real.log ↑N) / Real.log ↑N) Filter.atTop (nhds c)

Reported activity

Reported by these sources. Not reviewed here.

• Subtle errors

  GPT-Erdős

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• argument

  VibeMathed

  Machine

  GPT-5.6 starships (Claude Fable 5 reviewer)

  Reported outcome

  candidate

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