erdos_886

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.

theorem erdos_886 :
    answer(sorry) ↔ ∀ ε > 0, ∃ K : ℕ, ∀ᶠ n in atTop, (Erdos886Divisors n ε 1).card ≤ K

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