The distribution of numbers with many ordered factorizations
Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 2, pp. 583-606.

Let g(n) be the number of ordered factorizations of n into numbers larger than 1. We find precise bounds on the positive moments of g. We use these results to estimate the number of nx satisfying g(n)x α for all positive α. In addition, let G(n) and g 𝒫 (n) be the number of ordered factorizations of n into distinct numbers larger than 1 and primes, respectively. We also bound the positive moments of G and g 𝒫 from below.

Soit g(n) le nombre de factorisations de n en produit ordonné de facteurs plus grands que 1. On trouve des bornes précises pour les moments positifs de g. On utilise ces résultats pour estimer le nombre de nx tels que g(n)x α pour tous les α positifs. En outre, soient G(n) et g 𝒫 (n) les nombres de factorisations de n en produit ordonné de facteurs distincts plus grands que 1 et en produit ordonné de facteurs premiers respectivement. On donne des bornes inférieures pour les moments positifs de G et g 𝒫 .

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Accepted:
Published online:
DOI: 10.5802/jtnb.1170
Classification: 11A25,  11A51,  11N37
Keywords: Ordered factorizations
Noah Lebowitz-Lockard 1

1 8330 Millman St. Philadelphia, PA, 19118, United States
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Noah Lebowitz-Lockard. The distribution of numbers with many ordered factorizations. Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 2, pp. 583-606. doi : 10.5802/jtnb.1170. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1170/

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