Erdős problem 886 · problems.science

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

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3 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

886.lean

Retained formal statement1 of 3

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

Erdős attributes this conjecture to Ruzsa.

FormalConjectures/ErdosProblems/886.leanErdos886.erdos_8861 lineExact file

1sorry ↔ ∀ ε > 0, ∃ K, ∀ᶠ (n : ℕ) in Filter.atTop, (Erdos886.Erdos886Divisors n ε 1).card ≤ K

OpenStatement only, no proof