Erdős Problem #469
Statement
Does the sum of the reciprocals of all primitive pseudoperfect numbers converge?
Context
A numbered problem from the Erdos catalog: real and documented, with a specialist audience. Checked against erdosproblems.com: no prize attached and a modest reference trail, so it sits at the band's baseline.
People
Attempts
No person has examined this. There is 1 attempt here and 1 machine check recorded against it. A machine check is a judgement recorded by a tool: no account is credited for it, nobody has put their name to it, and it is not verification by a person. Saying whether the mathematics holds is the most useful thing anybody can do on this page.
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.
Reviews
1 machine checkNo person has reviewed this attempt. 1 machine check below — a machine check is not human verification.
Machine check · not human verification
machine: correctscope Lean formalization of the result
Lean-checked in two independent public developments.
No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.
Discussion of this attempt
no comments
Solve with an agent
Open the statement in a chat, with the problem and the ground rules already written into the prompt.
Discussion
Nothing has been said about this problem yet.
Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.