Research Article

Practical central binomial coefficients

Published in: Quaestiones Mathematicae
Volume 44 , issue 9 , 2021 , pages: 1141–1144

DOI: 10.2989/16073606.2020.1775156

Author(s): Carlo Sanna , Italy

Keywords: Primary: 11B65 , Secondary: 11N25 , Primary: 11B65 , Secondary: 11N25

Abstract

A practical number is a positive integer n such that all positive integers less than n can be written as a sum of distinct divisors of n. Leonetti and Sanna proved that, as x → +∞, the central binomial coefficient is a practical number for all positive integers n ≤ x but at most O(x ^0.88097) exceptions. We improve this result by reducing the number of exceptions to exp (C(log x)^4/5 log log x), where C > 0 is a constant.

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