A hybrid inequality for the number of divisors of an integer

TL;DR

This paper introduces a new explicit inequality relating the number of divisors of an integer to its size and prime divisor count, providing a novel mathematical bound.

Contribution

It presents a hybrid inequality that combines the integer's magnitude and prime divisor count to bound its number of divisors, advancing divisor function theory.

Findings

Derived an explicit inequality for divisor counts

Connects divisor count with prime factorization properties

Provides bounds useful for number theory applications

Abstract

We establish an explicit inequality for the number of divisors of an integer $n$. It uses the size of $n$ and its number of distinct prime divisors.