Abundant number

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Definition

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

Example

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.

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