Special Highly Composite Number/Examples/1

Example of Special Highly Composite Number

$1$ is a special highly composite number, being a highly composite number which is a divisor of all larger highly composite numbers.

Proof

We have that $1$ is highly composite.

From One Divides all Integers, it follows trivially that $1$ is a divisor of all larger highly composite numbers.

Thus, by definition, $1$ is a special highly composite number.

$\blacksquare$

Sources

• Dec. 1991: Steven Ratering: An Interesting Subset of the Highly Composite Numbers (Math. Mag. Vol. 64, no. 5: pp. 343 – 346)  www.jstor.org/stable/2690653