Source labels openChecked July 26, 2026

Erdős Problem 412

Let $σ_1(n)=σ(n)$ , the sum of divisors function, and $σ_k(n) = σ(σ_{k-1}(n))$ . Is it true that, for every $m, n ≥ 2$ , there exist some $i, j$ such that $σ_i(m) = σ_j(n)$ ?

Number theory AMS 11

Mathematical statement

Let $σ_1(n)=σ(n)$ , the sum of divisors function, and $σ_k(n) = σ(σ_{k-1}(n))$ . Is it true that, for every $m, n ≥ 2$ , there exist some $i, j$ such that $σ_i(m) = σ_j(n)$ ?

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_412

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_412 : answer(sorry) ↔ ∀ᵉ (m ≥ 2) (n ≥ 2), ∃ i j, (σ 1)^[i] m = (σ 1)^[j] n := 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/412background