Archivio Istituzionale della RicercaA 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 (Figure presented.) is a practical number for all positive integers n ≤ x but at most O(x0.88097) 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.
Practical central binomial coefficients / Sanna, Carlo. - In: QUAESTIONES MATHEMATICAE. - ISSN 1607-3606. - ELETTRONICO. - 44:9(2022), pp. 1141-1144. [10.2989/16073606.2020.1775156]
Practical central binomial coefficients
Carlo Sanna
2022
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 (Figure presented.) is a practical number for all positive integers n ≤ x but at most O(x0.88097) 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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https://hdl.handle.net/11583/2883058