Problem 469

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claims/: The 1 claim page of Problem 469, one per claimant's result; the problem's standing derives from them.

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Statement. Let $A$ be the set of all $n$ such that $n=d_1+\cdots+d_k$ with $d_i$ distinct proper divisors of $n$, but this is not true for any $m\mid n$ with $m<n$. Does

$$\sum_{n\in A}\frac{1}{n}$$

converge?

Status. PROVED (LEAN) on the site: the curator credits the convergence to Zachary J. Lewis, working with GPT 5.6 and Claude Fable 5, whose manuscript of July 2026 comes with a kernel-checked Lean development that Boris Alexeev verified and added to his repository; see the claim page. The standing in the frontmatter derives from the claim pages.

Source. erdosproblems.com/469, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #469, https://www.erdosproblems.com/469.

References.

• [BeEr74] Benkoski, S. J. and Erdős, P., On weird and pseudoperfect numbers. Math. Comp. (1974), 617-623.

Formalization. Statement in formal-conjectures. The author's Lean 4 proof, a single-file version produced with Aristotle of Harmonic, and the version in Boris Alexeev's repository of formalized Erdős problems are linked from the claim page at pinned commits; this corpus has built and audited none of them.

Progress

Not yet compiled.

Known Results

Not yet compiled.

Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

• benkoski_1974_weird_pseudoperfect_numbers