ABSTRACT
Suppose that you are playing with sums of divisors of numbers (yes, mathematicians do things like this) and you discover the following two examples:
1 + 2 + 3 = 6
1 + 2 + 4 + 7 + 14 = 28.
What is so special about these? 1, 2, 4, 7, 14 are the positive divisors of 28 that are less than 28. Similarly, 1, 2, 3 are the divisors of 6 that are less than 6. Are there any other such examples? In fact, here is another:
1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496.
