erdos_1084_upper_lower_d3

Erdős claims the existence of two constants $c_1, c_2 > 0$ such that $6n - c_1 n^{2/3} ≤ f_3(n) \le 6n - c_2 n^{2/3}$.

theorem erdos_1084_upper_lower_d3 :
    ∃ c₁ : ℝ, ∃ c₂ > (0 : ℝ), ∀ᶠ n in atTop,
      6 * n - c₁ * n ^ (2 / 3 : ℝ) ≤ f 3 n ∧ f 3 n ≤ 6 * n - c₂ * n ^ (2 / 3 : ℝ)

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