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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692.lean

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Cambie has calculated that unimodularity fails even for $n=2$ and $n=3$ . For example, $\delta_1(3,6)= 0.35\quad \delta_1(3,7)\approx 0.33\quad \delta_1(3,8)\approx 0.3619.$

FormalConjectures/ErdosProblems/692.leanErdos692.erdos_692.variants.cambie_three1 lineExact file

1∀ (δ : ℕ → ℕ → ℝ), (∀ (a b : ℕ), Erdos692.IsDelta₁ a b (δ a b)) → δ 3 7 < δ 3 6 ∧ δ 3 7 < δ 3 8

SolvedStatement only, no proof

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