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.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Sanna_20170821.pdf
accesso aperto
Tipologia:
1. Preprint / submitted version [pre- review]
Licenza:
PUBBLICO - Tutti i diritti riservati
Dimensione
264.88 kB
Formato
Adobe PDF
|
264.88 kB | Adobe PDF | Visualizza/Apri |
|
Central binomial coefficients divisible by or coprime to their indices.pdf
non disponibili
Tipologia:
2a Post-print versione editoriale / Version of Record
Licenza:
Non Pubblico - Accesso privato/ristretto
Dimensione
155.17 kB
Formato
Adobe PDF
|
155.17 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
Utilizza questo identificativo per citare o creare un link a questo documento:
https://hdl.handle.net/11583/2722660