abundant number

An integer n is an abundant number if the sum of the proper divisors of n is more than n itself, or the sum of all the divisorsMathworldPlanetmathPlanetmath is more than twice n. That is, σ(n)>2n, with σ(n) 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 x gives an abundant number (as long as x>1).

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