# Definition:Special Highly Composite Number

## Contents

## Definition

A **special highly composite number** is a highly composite number which is a divisor of all larger highly composite numbers.

### Sequence

The sequence of special highly composite numbers consists of:

- $1, 2, 6, 12, 60, 2520$

This sequence is A106037 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

## Examples

### $1$ is a 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.

### $2$ is a Special Highly Composite Number

$2$ is a special highly composite number, being a highly composite number which is a divisor of all larger highly composite numbers.

### $6$ is a Special Highly Composite Number

$6$ is a special highly composite number, being a highly composite number which is a divisor of all larger highly composite numbers.

### $12$ is a Special Highly Composite Number

$12$ is a special highly composite number, being a highly composite number which is a divisor of all larger highly composite numbers.

### $60$ is a Special Highly Composite Number

$60$ is a special highly composite number, being a highly composite number which is a divisor of all larger highly composite numbers.

### $2520$ is a Special Highly Composite Number

$2520$ is a special highly composite number, being a highly composite number which is a divisor of all larger highly composite numbers.

## Sources

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