Definition:Special Highly Composite Number

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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