What are "abundant" numbers? Why would such numbers be called plentiful? "Abundant" is a strange way to describe a number, and equally strange are descriptions such as "deficient," "perfect," and "amicable." But these descriptions of numbers came about because the ancient Greek mathematicians were intrigued by certain characteristics of positive integers.

The Greeks discovered, for example, that some numbers are equal to the sum of their divisors; for instance, 6 is equal to the sum of its proper divisors 3, 2, and 1. (Although 6 is a divisor of 6, it is not considered a "proper" divisor.) Greek mathematicians discovered a sense of balance or perfection in such numbers, and labeled them "perfect."

As an extension of the idea of perfect numbers, the concept of "abundant" and "deficient" numbers emerged. If the sum of the proper divisors of a number is greater than the...