Definitions for **"Abundant number"**

A number that is less than the sum of its factors (excluding itself). For example, the factors of 12 (1, 2, 3, 4, 6) add up to 16. Compare deficient number, perfect number.

(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.

A positive integer that is smaller than the sum of its proper divisors.