Problem 469

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?

Source: erdosproblems.com/469

Number theory
Divisors

Wiki page

Status

SolvedProved

An accepted solution exists. The statement is true.

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 (Lewis, 2026). The standing in the frontmatter derives from the claim pages.

Problem 469

Status

Proof claims

Discussion