erdos_208.i

Let $s_1 < s_2 < \dots$ be the sequence of squarefree numbers. Is it true that for any $\epsilon > 0$ and large $n$, $s_{n+1} - s_n \ll_\epsilon s_n^\epsilon$?

theorem erdos_208.i : answer(sorry) ↔
    ∀ ε > (0 : ℝ), (fun n => (s (n + 1) - s n : ℝ)) =O[atTop] (fun n => (s n : ℝ)^ε)

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