Archivio Istituzionale della RicercaLet A be the set of all positive integers n such that n divides the central binomial coefficient (2nn). Pomerance proved that the upper density of A is at most 1−log2. We improve this bound to 1−log2−0.05551. Moreover, let B be the set of all positive integers n such that n and (2nn) are relatively prime. We show that #(B∩[1,x])≪x/logx−−−−√ for all x>1.
Central binomial coefficients divisible by or coprime to their indices / Sanna, Carlo. - In: INTERNATIONAL JOURNAL OF NUMBER THEORY. - ISSN 1793-0421. - STAMPA. - 14:4(2018), pp. 1135-1141. [10.1142/S1793042118500707]
Central binomial coefficients divisible by or coprime to their indices
Sanna, Carlo
2018
Abstract
Let A be the set of all positive integers n such that n divides the central binomial coefficient (2nn). Pomerance proved that the upper density of A is at most 1−log2. We improve this bound to 1−log2−0.05551. Moreover, let B be the set of all positive integers n such that n and (2nn) are relatively prime. We show that #(B∩[1,x])≪x/logx−−−−√ for all x>1.
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Utilizza questo identificativo per citare o creare un link a questo documento:
https://hdl.handle.net/11583/2722660