Abundant number

Definition

An abundant number is any number, n, which has a sigma value greater than 2n.

Example

The divisors of 12 are $(1,2,3,4,6,12)$, so

$\sigma (12)=1+2+3+4+6+12=28$

Abundant numbers and aliquot sequences

Abundant numbers increase the size of an aliquot sequence because when an abundant number occurs in a sequence, the next step is larger than the current step. Also, when a sequence is controlled by a driver, the subsequent steps are always abundant until an escape from the driver is obtained.

External links

• Wikipedia