Definition:Special Highly Composite Number
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.
Also see
- Results about special highly composite numbers can be found here.
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