erdos_377.variants.ae

Erdos, Graham, Ruzsa, and Straus proved that if $$ f(n) = \sum_{p \leq n} 1_{p\nmid {2n \choose n}}\frac{1}{p} $$ and $$ \gamma_0 = \sum_{k = 2}^{\infty} \frac{\log k}{2^k} $$ then for almost all integers $f(m) = \gamma_0 + o(1)$. [EGRS75] Erdős, P. and Graham, R. L. and Ruzsa, I. Z. and Straus, E. G., _On the prime factors of $\binom{2n}{n}$_. Math. Comp. (1975), 83-92.

theorem erdos_377.variants.ae (γ₀ : ℝ) (hγ₀ : γ₀ = ∑' (k : ℕ), (k + 2 : ℝ).log / 2 ^ (k + 2)) :
    ∃ (o : ℕ → ℝ) (_ : Tendsto o atTop (𝓝 0)),
      ∀ᶠ n in cofinite, sumInvPrimesNotDvdCentralBinom n = γ₀ + o n

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