(4) A number in which the sum of all its proper factors is greater than the number itself. Example: 12 is an abundant number because the sum of its proper factors is 1 + 2 + 3 + 4 + 6 = 16 and 16 is greater than 12.
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 Ïƒ(n) > 2n. Here Ïƒ(n) is the divisor function: the sum of all positive divisors of n, including n itself. The value Ïƒ(n) − 2n is called the abundance of n.