An abundant number is a positive integer that has a sum of its proper divisors greater than itself. Proper divisors are the positive divisors of a number excluding the number itself. For example, the number 12 has proper divisors 1, 2, 3, 4, 6, and their sum is 16, which is greater than 12. Abundant numbers are part of a broader category of integers known as deficient numbers and perfect numbers. A deficient number has a sum of proper divisors less than itself, while a perfect number has a sum equal to itself. The study of abundant numbers is important in number theory.