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 statement2 of 5

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

FormalConjectures/ErdosProblems/692.leanErdos692.erdos_692.parts.ii2 linesExact file

1∀ (n : ℕ) (δ : ℕ → ℕ → ℝ),2  (∀ (a b : ℕ), Erdos692.IsDelta₁ a b (δ a b)) → IsGreatest (δ n '' Set.Ioi (n + 1)) (δ n sorry)

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