Erdős problem 692 · problems.science

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

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

692.lean

Retained formal statement3 of 5

Cambie [Ca25] has shown that, for fixed $n$ , the sequence $\delta_1(n,m)$ has superpolynomially many local maxima $m$ .

FormalConjectures/ErdosProblems/692.leanErdos692.erdos_692.variants.cambie_local_maxima3 linesExact file

1∀ (k : ℕ) (δ : ℕ → ℕ → ℝ),2  (∀ (a b : ℕ), Erdos692.IsDelta₁ a b (δ a b)) →3    ∀ᶠ (n : ℕ) in Filter.atTop, ↑n ^ k ≤ ↑{m | n + 1 < m ∧ δ n (m - 1) ≤ δ n m ∧ δ n (m + 1) ≤ δ n m}.ncard

SolvedStatement only, no proof

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