Erdős Problem #469
Erdős problem #469 · erdosproblems.com/469
Does the sum of the reciprocals of all primitive pseudoperfect numbers converge?
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Number Theory, Divisors
- Posed by
- SJ Benkoski, Paul Erdos
- Year posed
- 1974
- Years open
- 52y
- Solved
- 2026-07-21
- Model
- GPT-5.6 Sol Ultra, Claude Fable 5
- Vendor
- OpenAI / Anthropic
- Collaborators
- Zachary J. Lewis
- Verification
- Lean-verified
- Publication
- Announced
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
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.
Verification
Lean-checked in two independent public developments.
Sources
- Lean proofGitHub repo of the proof
- TranscriptLewis' preprint on GitHub
- Problem recorderdosproblems.com/469Benkoski & Erdos 1974 - Problem statement