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 $f(n) = \sum_{p \leq n} 1_{p\nmid {2n \choose n}}\frac{1}{p}$ then there is some constant $c < 1$ such that for all large $n$ $f(n) \leq c \log\log n.$

[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.ub1 lineExact file

1∃ c < 1, ∀ᶠ (n : ℕ) in Filter.atTop, Erdos377.sumInvPrimesNotDvdCentralBinom n ≤ c * Real.log (Real.log ↑n)

SolvedStatement only, no proof

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