Source labels openChecked July 26, 2026

Erdős Problem 291: I

Let $n\geq 1$ and define $L_n$ to be the least common multiple of $\{1,\ldots,n\}$ and $a_n$ by $\sum_{1\leq k\leq n}\frac{1}{k}=\frac{a_n}{L_n}$ .

Number theory AMS 11

Mathematical statement

Let $n\geq 1$ and define $L_n$ to be the least common multiple of $\{1,\ldots,n\}$ and $a_n$ by $\sum_{1\leq k\leq n}\frac{1}{k}=\frac{a_n}{L_n}$ .

Is it true that $(a_n,L_n)=1$ occurs for infinitely many $n$ ?

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.parts.i

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_291.parts.i :    answer(sorry) ↔      { n : ℕ | Nat.gcd (a n) (L n) = 1 }.Infinite := 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