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On the Number of Polynomials with Coefficients In [n] Cover

On the Number of Polynomials with Coefficients In [n]

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică
Volume 22 (2014): Issue 1 (March 2014)
By: Dorin Andrica and  Eugen J. Ionascu  
Open Access
|Dec 2014

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}.

DOI: https://doi.org/10.2478/auom-2014-0001 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
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Language: English
Page range: 13 - 23
Submitted on: Sep 1, 2013
Accepted on: Dec 1, 2013
Published on: Dec 10, 2014
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year
Keywords:
Dirichlet divisor problem,
number of positive integer divisors,
the sequence (),
asymptotic formula
Related subjects:
Mathematics,
General mathematics

© 2014 Dorin Andrica, Eugen J. Ionascu, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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