Bounds for the counting function of the Jordan-Pólya numbers

Jean-Marie De Koninck, Nicolas Doyon, A. Arthur Bonkli Razafindrasoanaivolala, and William Verreault

Address: Corresponding author: J.-M. De Koninck, Département de mathématiques et de statistique, Université Laval, Québec G1V 0A6, Canada nicolas.doyon@mat.ulaval.ca   arthur@aims.edu.gh william.verreault.2@ulaval.ca

E-mail: jmdk@mat.ulaval.ca

Abstract: A positive integer $n$ is said to be a Jordan-Pólya number if it can be written as a product of factorials. We obtain non-trivial lower and upper bounds for the number of Jordan-Pólya numbers not exceeding a given number $x$.

AMSclassification: primary 11B65; secondary 11A41, 11A51, 11N05.

Keywords: Jordan-Pólya numbers, factorial function, friable numbers.

DOI: 10.5817/AM2020-3-141