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Erdős problem 692

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Let δ1(n,m)\delta_1(n,m) be the density of the set of integers with exactly one divisor in (n,m)(n,m). Is δ1(n,m)\delta_1(n,m) unimodular for m>n+1m>n+1 (i.e. increases until some mm then decreases thereafter)?

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FormalConjectures/ErdosProblems/

692.lean

Retained formal statement2 of 5

Let δ1(n,m)\delta_1(n,m) be the density of the set of integers with exactly one divisor in (n,m)(n,m). For fixed nn, where does δ1(n,m)\delta_1(n,m) achieve its maximum?

FormalConjectures/ErdosProblems/692.leanErdos692.erdos_692.parts.ii2 linesExact file
∀ (n : ℕ) (δ : ℕ → ℕ → ℝ),  (∀ (a b : ℕ), Erdos692.IsDelta₁ a b (δ a b)) → IsGreatest (δ n '' Set.Ioi (n + 1)) (δ n sorry)
OpenStatement only, no proof