The distribution of numbers with many ordered factorizations
Noah Lebowitz-Lockard1
1 8330 Millman St. Philadelphia, PA, 19118, United States
Journal de théorie des nombres de Bordeaux, Tome 33 (2021) no. 2, pp. 583-606.

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 n≤x 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 .

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 n≤x 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.

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DOI : 10.5802/jtnb.1170
Classification : 11A25, 11A51, 11N37
Mots clés : Ordered factorizations
Noah Lebowitz-Lockard 1

1 8330 Millman St. Philadelphia, PA, 19118, United States
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Noah Lebowitz-Lockard. The distribution of numbers with many ordered factorizations. Journal de théorie des nombres de Bordeaux, Tome 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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