Skip to content

Erdős problem 538

If each integer has at most rr representations m=pam = pa with pp prime and a∈A⊆[1,N]a \in A \subseteq [1, N], what is the best upper bound for ∑a∈A1/a\sum_{a \in A} 1/a? The candidate proof gives the matching order Θr(log⁡N/log⁡log⁡N)\Theta_r(\log N / \log\log N).

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/538.lean

Formal Conjectures

FormalConjectures/ErdosProblems/538.leanErdos538.erdos_5386 linesExact file
True ↔  ∀ (r : ℕ),    2 ≤ r →      ∃ c,        0 < c ∧          Filter.Tendsto (fun N => Erdos538.maxMass r N * Real.log (Real.log ↑N) / Real.log ↑N) Filter.atTop (nhds c)
OpenStatement only, no proof

Proof manifests naming this Problem

  • William Blair Lean proofswilliamjblair:Erdos538.erdos538_matching_order

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

Continue

Start a contributionBrowse the source filesOpen the collection entry

Search problems.science

Find a Problem, Result, source, or page