All open problems
Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

Erdős Problem 394: Ii

Is it true that, for k2k\geq 2, nxtk+1(n)=o(nxtk(n))?\sum_{n\leq x}t_{k+1}(n) =o\left(\sum_{n\leq x}t_k(n)\right)?

Mathematical statement

Is it true that, for k2k\geq 2, nxtk+1(n)=o(nxtk(n))?\sum_{n\leq x}t_{k+1}(n) =o\left(\sum_{n\leq x}t_k(n)\right)?

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_394.parts.ii

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_394.parts.ii :    answer(sorry)        k  2, (fun (x : )  ∑ n  Icc 1 ⌊x⌋₊,      (t (k + 1) n : )) =o[atTop]      (fun (x : )  ∑ n  Icc 1 ⌊x⌋₊,      (t k 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