| Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3). |
Navigation
| Topics | Help • Register • News • History • How to • Sequences statistics • Template prototypes |
Difference between revisions of "Abundant number"
(restored) |
(Recategorizing) |
||
| Line 11: | Line 11: | ||
==External links== | ==External links== | ||
*[[Wikipedia:Abundant_number|Wikipedia]] | *[[Wikipedia:Abundant_number|Wikipedia]] | ||
| − | [[Category: | + | |
| + | [[Category:Number]] | ||
Latest revision as of 00:58, 11 August 2024
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.
