Garrett Dubofsky

A natural number is perfect if it is equal to the sum of its proper divisors. The most famous example is 6 = 1 + 2 + 3. We will explore these perfect numbers and other related classes of natural numbers using the arithmetic "sum of divisors" and abundancy index functions. These functions are then used to prove the sum of the reciprocals of all the primes diverges, among other intriguing results. We will then investigate the natural density of a set, its properties, and the implications for these types of numbers.