Chapter 2.1, Problem 10MS

Perfect numbers. The only natural numbers that divide evenly into 6. Other than 6 itself, are 1, 2, and 3. Notice that the sum of all those numbers equals the original number $6\left(1+2+3=6\right).$ What is the next number that has the property of equaling the sum of all the natural numbers other than itself that divide evenly into it? Such numbers are called perfect numbers. No one knows whether or not there are infinitely many perfect numbers. In fact, no one knows whether there are any odd perfect numbers. These two unsolved mysteries are examples of longstanding open questions in the theory of numbers.