Divisibility of the central binomial coefficient $\binom{2n}{n}$

Publication date: 9 September 2019

Abstract: We show that for every fixed

e l l i n m a t h b b N

, the set of

n

with

has a positive asymptotic density

c_{e} l l

, and we give an asymptotic formula for

c_{e} l l

as

e l l o i n f t y

. We also show that

for some constant

c

. One novelty is a method to capture the effect of large prime factors of integers in general sequences.

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