Source labels openChecked July 26, 2026

Erdős Problem 400: Ii

Is it true that there is a constant $c_k$ such that for almost all $n < x$ we have $g_k(n)=c_k\log x+o(\log x)$ ?

Number theory AMS 11

Mathematical statement

Is it true that there is a constant $c_k$ such that for almost all $n < x$ we have $g_k(n)=c_k\log x+o(\log x)$ ?

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_400.parts.ii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_400.parts.ii :    answer(sorry) ↔ ∀ᵉ (k ≥ 2), ∃ c : ℝ, ∀ ε > 0,      Tendsto (fun x : ℕ ↦        (((Icc 1 x).filter (fun n ↦          |(g k n : ℝ) - c * Real.log x| ≤ ε * Real.log x)).card : ℝ) / x)        atTop (𝓝 1) := 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/400background