Source labels openChecked July 26, 2026

Erdős Problem 469

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?

Number theory AMS 11

Mathematical statement

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?

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_469

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_469 :    letI A := {n : ℕ | 0 < n ∧ n.IsSumDivisors ∧ ∀ m < n, m ∣ n → ¬ m.IsSumDivisors}    answer(sorry) ↔ Summable fun n : A ↦ 1 / (n : ℝ) := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/469background