erdos_325.variants.weaker

Writing $f_{k, 3}(x)$ for the number of integers $\leq x$ which are the sum of three $k$th powers, is it even true that $f_{k, 3}(x) \gg_{\epsilon} x ^ (3 / k - \epsilon)$?

theorem erdos_325.variants.weaker :
    answer(sorry) ↔ ∀ ε > 0, ∀ k : ℕ, 3 ≤ k → (fun x : ℕ => (x : ℝ) ^ ((3 / k : ℝ) - ε)) =O[atTop]
      (fun x => (cardIsSumThreePowerBelow k x : ℝ))

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