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New upper bounds for the number of divisors function

Volume 162 / 2020

Jean-Marie De Koninck, Patrick Letendre Colloquium Mathematicum 162 (2020), 23-52 MSC: 11N37, 11N56. DOI: 10.4064/cm7792-6-2019 Published online: 3 April 2020

Abstract

Let $\tau (n)$ stand for the number of divisors of the positive integer $n$. We obtain upper bounds for $\tau (n)$ in terms of $\log n$ and the number of distinct prime factors of $n$.

Authors

  • Jean-Marie De KoninckDépartement de Mathématiques et de Statistique
    Université Laval
    Pavillon Alexandre-Vachon
    1045 Avenue de la Médecine
    Québec, QC G1V 0A6, Canada
    e-mail
  • Patrick LetendreDépartement de Mathématiques et de Statistique
    Université Laval
    Pavillon Alexandre-Vachon
    1045 Avenue de la Médecine
    Québec, QC G1V 0A6, Canada
    e-mail

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