Problem 377

Is there some absolute constant $C>0$ such that

\sum_{p\leq n}1_{p\nmid \binom{2n}{n}}\frac{1}{p}\leq C

for all $n$ (where the summation is restricted to primes $p\leq n$ )?

Status

Open

No claim settles this problem.

EGRS75: Erdős, P. and Graham, R. L. and Ruzsa, I. Z. and Straus, E. G., On the prime factors of $(\sp{2n}\sb{n})$ . Math. Comp. (1975), 83-92.
Gu04: Guy, Richard K., Unsolved problems in number theory. Third edition, Problem Books in Mathematics, Springer, New York (2004), xviii+437 pp.; doi:10.1007/978-0-387-26677-0. Section B33 "Largest divisor of a binomial coefficient", printed p. 135, where the book states the Erdős, Graham, Ruzsa and Straus conjecture. Library home: Guy 2004.