Source labels openChecked July 26, 2026

Erdős Problem 647: Lim

Erdős says 'it is extremely doubtful' that there are infinitely many such $n$ , and in fact suggests that $lim_{n\to\infty} \max_{m < n}(\tau(m) + m − n) = \infty.$

Number theory AMS 11

Mathematical statement

Erdős says 'it is extremely doubtful' that there are infinitely many such $n$ , and in fact suggests that

lim_{n\to\infty} \max_{m < n}(\tau(m) + m − n) = \infty.

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_647.variants.lim

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_647.variants.lim :    answer(sorry) ↔ atTop.Tendsto (fun n ↦ ⨆ m : Fin n, σ 0 m + m - n) atTop := 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/647background