The board / number theory / #469
Erdős Problem #469
PROVED LEANdatabase updated 2026-07-21
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The proposition that `n` is a sum of distinct proper divisors.
Let \(A\) be the set of all \(n\) such that \(n = d_1 + ⋯ + d_k\) with \(d_i\) distinct proper divisors of \(n\), but this is not true for any \(m ∣ n\) with \(m < n\). Does: \[ \sum_{n ∈ A} \frac 1 n \] converge? Yes: the sum converges. This was proved by Lewis [Le25], whose proof has been formalized in Lean.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/469.Prizenone
Topicsnumber theory, divisors
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/469
Attempts
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