a composite number whose factors, without the number itself, have a sum greater than the number

a positive integer for which the sum of its proper divisors is greater that the number

An abundant number (also called a redundant number) is number (an integer) for which the sum of its proper factors ( divisors) is greater than the number itself. For example, 12 is an abundant number because the proper divisors of 12 are 1, 2, 3, 4, 6, which add up to 16, which is greater than 12. Compare with perfect number, deficient number.

In mathematics, an abundant number or excessive number is a number n for which σ(n) > 2n. Here σ(n) is the divisor function: the sum of all positive divisors of n, including n itself. The value σ(n) − 2n is called the abundance of n.