Abstract: Ancient Greek mathematicians were fond of numbers whose whole is exactly the sum of its parts, that is, numbers such as 6 whose proper divisors sum to the number itself. So much so that they called these numbers perfect. Despite years of study, we still do not know much about the distribution of perfect numbers. In this talk we will look at generalizations of perfect numbers, the amicable and sociable numbers, and see what we now know about the distribution of these numbers.

Click here to see a related XKCD comic.