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 statement5 of 5

Erdős proved that $\delta_1(n,m) \ll \frac{1}{(\log n)^c}$ for all $m$ , for some constant $c>0$ .

FormalConjectures/ErdosProblems/692.leanErdos692.erdos_692.variants.erdos_upper_bound3 linesExact file

1∀ (δ : ℕ → ℕ → ℝ),2  (∀ (a b : ℕ), Erdos692.IsDelta₁ a b (δ a b)) →3    ∃ c > 0, ∃ C > 0, ∀ᶠ (n : ℕ) in Filter.atTop, ∀ (m : ℕ), δ n m ≤ C / Real.log ↑n ^ c

SolvedStatement only, no proof

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