Source labels openChecked July 26, 2026

Erdős Problem 291: Shiu Heuristic Asymptotic

This leads to a heuristic prediction (see for example a preprint of Shiu [Sh16]) of $\asymp\frac{x}{\log x}$ for the number of $n\in [1,x]$ such that $(a_n,L_n)=1$ .

Number theory AMS 11

Mathematical statement

This leads to a heuristic prediction (see for example a preprint of Shiu [Sh16]) of $\asymp\frac{x}{\log x}$ for the number of $n\in [1,x]$ such that $(a_n,L_n)=1$ .

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_291.variants.shiu_heuristic_asymptotic

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_291.variants.shiu_heuristic_asymptotic :    Asymptotics.IsTheta atTop      (fun x : ℕ ↦ ((((Finset.Icc 1 x).filter (fun n ↦ Nat.gcd (a n) (L n) = 1)).card : ℝ)))      (fun x : ℕ ↦ (x : ℝ) / 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/291background