abundant number
An integer is an abundant number if the sum of the proper divisors of is more than itself, or the sum of all the divisors is more than twice . That is, , with being the sum of divisors function.
For example, the integer 30. Its proper divisors are 1, 2, 3, 5, 6, 10, 15, which add up to 42.
Multiplying a perfect number by some integer gives an abundant number (as long as ).
Given a pair of amicable numbers, the lesser of the two is abundant, its proper divisors adding up to the greater of the two.
Title | abundant number |
---|---|
Canonical name | AbundantNumber |
Date of creation | 2013-03-22 15:52:21 |
Last modified on | 2013-03-22 15:52:21 |
Owner | CompositeFan (12809) |
Last modified by | CompositeFan (12809) |
Numerical id | 6 |
Author | CompositeFan (12809) |
Entry type | Definition |
Classification | msc 11A05 |
Related topic | AmicableNumbers |