Note: Due to changes in the Riesel prime template, most of those pages (and related) are not shown properly.
This will take some time!
Wanna help? Please move any Riesel prime page first, then edit/add the base parameter.
Navigation
Topics Register • News • History • How to • Sequences statistics • Template prototypes

Abundant number

From Prime-Wiki
Jump to: navigation, search

Definition

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

Example

The divisors of 12 are [math]\displaystyle{ (1, 2, 3, 4, 6, 12) }[/math], so

[math]\displaystyle{ \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.

External links