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Erdős problem 942

Let h(n)h(n) count powerful integers in [n2,(n+1)2)[n^2, (n+1)^2). What is the extremal order of h(n)h(n)?

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

Retained declaration

FormalConjectures/ErdosProblems/942.lean

Formal Conjectures

FormalConjectures/ErdosProblems/942.leanErdos942.erdos_9426 linesExact file
True ↔  ∃ c > 0,    ∃ o,      o =o[Filter.atTop] 1 ∧        (∀ᶠ (n : ℕ) in Filter.atTop, ↑(Erdos942.erdos_942.h n) < Real.log ↑n ^ (c + o n)) ∧          {n | ↑(Erdos942.erdos_942.h n) > Real.log ↑n ^ (c - o n)}.Infinite
OpenStatement only, no proof

Reported activity

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

  • AI collaborating with humans

    Erdős AI contributions wiki · 13-14 Jun, 2026

    Machine
    Aristotle, Claude Opus 4.8, Codex, GPT-5.5
    People
    Scott Hughes
    Open the source record

  • AI building on literature

    Erdős AI contributions wiki · 23 Nov, 2025

    Machine
    Gemini
    Open the source record

  • argument

    VibeMathed

    Machine
    Claude, Codex, Aristotle
    Reported outcome
    partial
    Open the source record

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