An abundant number is any number, n, which has a sigma value greater than 2n.
The divisors of 12 are [math](1, 2, 3, 4, 6, 12)[/math], so
- [math]\sigma(12)\ =\ 1+2+3+4+6+12\ =\ 28[/math]
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.