New upper bounds for the number of divisors function
Volume 162 / 2020
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 $n$.
