Journal of Integer Sequences, Vol. 14 (2011), Article 11.3.3

Powerful Values of Quadratic Polynomials

Jean-Marie De Koninck and Nicolas Doyon
Départment de Mathématiques
Université Laval
Québec, PQ G1V 0A6

Florian Luca
Instituto de Matemáticas
Universidad Nacional Autónoma de México
C. P. 58180
Morelia, Michoacán


We study the set of those integers k such that n2 + k is powerful for infinitely many positive integers n. We prove that most integers k have this property.

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(Concerned with sequence A001694.)

Received October 27 2010; revised version received February 22 2011. Published in Journal of Integer Sequences, March 25 2011.

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