erdos_489.variants.squarefree

When $A = \{p^2 : p \textrm{ prime}\}$, $B$ is the set of squarefree numbers, and the existence of this limit was proved by Erdős. This is the $\alpha = 2$ case of Erdős Problem 145.

theorem erdos_489.variants.squarefree :
    ∃ L : ℝ, Tendsto
      (fun x : ℕ => GapSumSq {n | ∃ p, Nat.Prime p ∧ n = p ^ 2} x / (x : ℝ))
      atTop (𝓝 L)

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