Definition:Highly Composite Number

Definition
Let $n \in \Z_{>0}$ be a positive integer.

Then $n$ is highly composite :
 * $\forall m \in \Z_{>0}, m < n: \map \tau m < \map \tau n$

where $\map \tau n$ is the divisor counting (tau) function of $n$.

That is, $n$ has a larger number of divisors than any smaller positive integer.

Also known as
Some sources use the term highly abundant number, but uses that term for a different concept.