Source labels openChecked July 26, 2026

Erdős Problem 400: I

Can one show that $\sum_{n\leq x}g_k(n) \sim c_k x\log x$ for some constant $c_k$ ?

Number theory AMS 11

Mathematical statement

Can one show that $\sum_{n\leq x}g_k(n) \sim c_k x\log x$ for some constant $c_k$ ?

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.i

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_400.parts.i :    answer(sorry) ↔ ∀ᵉ (k ≥ 2), ∃ c : ℝ,      (fun x : ℕ ↦ (∑ n ∈ Icc 1 x, (g k n : ℝ))) ~[atTop]      (fun x : ℕ ↦ c * x * Real.log x) := 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