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Erdős Problem #469

Number theory · solved

2 comments

Statement

Does the sum of the reciprocals of all primitive pseudoperfect numbers converge?

Record

Source
Added

Comments

No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    Zachary J. Lewis, using GPT-5.6 Sol Ultra, Claude Fable 5

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The public proof, which also yields density results for pseudoperfect numbers, was developed with GPT-5.6 Sol Ultra and reviewed with Claude Fable 5.

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    Lean-checked in two independent public developments.

    Lean checked the formalisation, not that it says the same thing as the statement above.

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Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.