Erdős problem 377 · problems.science

Is there some absolute constant $C > 0$ such that $\sum_{p \leq n} 1_{p\nmid {2n \choose n}}\frac{1}{p} \leq C$ for all $n$ ?

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FormalConjectures/ErdosProblems/

377.lean

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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.

FormalConjectures/ErdosProblems/377.leanErdos377.erdos_377.variants.ae5 linesExact file

1∀ (γ₀ : ℝ),2  γ₀ = ∑' (k : ℕ), Real.log (↑k + 2) / 2 ^ (k + 2) →3    ∃ o,4      ∃ (_ : Filter.Tendsto o Filter.atTop (nhds 0)),5        ∀ᶠ (n : ℕ) in Filter.cofinite, Erdos377.sumInvPrimesNotDvdCentralBinom n = γ₀ + o n

SolvedStatement only, no proof

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