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Erdős problem 886

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Let ϵ>0\epsilon>0. Is it true that, for all large nn, the number of divisors of nn in (n1/2,n1/2+n1/2−ϵ)(n^{1/2},n^{1/2}+n^{1/2-\epsilon}) is Oϵ(1)O_\epsilon(1)?

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FormalConjectures/ErdosProblems/

886.lean

Retained formal statement1 of 3

Let ϵ>0\epsilon>0. Is it true that, for all large nn, the number of divisors of nn in (n1/2,n1/2+n1/2−ϵ)(n^{1/2},n^{1/2}+n^{1/2-\epsilon}) is Oϵ(1)O_\epsilon(1)?

Erdős attributes this conjecture to Ruzsa.

FormalConjectures/ErdosProblems/886.leanErdos886.erdos_8861 lineExact file
sorry ↔ ∀ ε > 0, ∃ K, ∀ᶠ (n : ℕ) in Filter.atTop, (Erdos886.Erdos886Divisors n ε 1).card ≤ K
OpenStatement only, no proof