Highly Composite Number/Examples/1

Example of Highly Composite Number

$1$ is a highly composite number, being the smallest positive integer with $1$ divisor or more.

Proof

From $\sigma_0$ of $1$:

$\map {\sigma_0} 1 = 1$

The positive integer $1$ has $1$ divisor, that is, $1$ itself.

Vacuously, no smaller positive integer has a greater number of divisors.

Thus, despite not actually being composite, $1$ is a highly composite number.

$\blacksquare$