<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we introduce several natural sequences related to polynomials of degree <italic>s</italic> having coefficients in {1,2, …,<italic>n</italic>} (<italic>n</italic> ∈ <bold>N</bold>) which factor completely over the integers. These sequences can be seen as generalizations of A006218. We provide precise methods for calculating the terms and investigate the asymptotic behavior of these sequences for <italic>s</italic> ∈ {1, 2, 3}.</p></abstract>

In this paper we introduce several natural sequences related to polynomials of degree s having coefficients in {1,2, …,n} (n ∈ N) which factor completely over the integers. These sequences can be seen as generalizations of A006218. We provide precise methods for calculating the terms and investigate the asymptotic behavior of these sequences for s ∈ {1, 2, 3}.

On the Number of Polynomials with Coefficients In [<italic>n</italic>]

Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Str. Kogalniceanu 1, 400084 Cluj-Napoca, Romania.

Department of Mathematics, Columbus State University, 4225 University Avenue, Columbus, GA 31907, USA.

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the Number of Polynomials with Coefficients In []

In this paper we introduce several natural sequences related to polynomials of degree s having coefficients in {1,2, …,n} (n ∈ N) which factor completely over...

On the Number of Polynomials with Coefficients In [n]

Publié en ligne: 10 déc. 2014

Pages: 13 - 23

Reçu: 01 sept. 2013

Accepté: 01 déc. 2013

DOI: https://doi.org/10.2478/auom-2014-0001

Mots clés
Dirichlet divisor problem, number of positive integer divisors, the sequence (), asymptotic formula

© 2014 Dorin Andrica and Eugen J. Ionascu

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the Number of Polynomials with Coefficients In [n]

Publié en ligne: 10 déc. 2014

Pages: 13 - 23

Reçu: 01 sept. 2013

Accepté: 01 déc. 2013

DOI: https://doi.org/10.2478/auom-2014-0001

Mots clésDirichlet divisor problem, number of positive integer divisors, the sequence (), asymptotic formula

© 2014 Dorin Andrica and Eugen J. Ionascu

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Dirichlet divisor problem, number of positive integer divisors, the sequence (), asymptotic formula