A natural number $$n$$ is said to be good if $$n$$ is the sum of $$r$$ consecutive positive integers, for some $$r \ge 2$$. Find the number of good numbers in the set $$\{1, 2, \ldots, 100\}$$.

A number is a sum of at least two consecutive positive integers exactly when it has an odd divisor greater than 1, that is, when it is not a power of 2. The powers of 2 in the given set are $$1, 2, 4, 8, 16, 32, 64$$, which is 7 numbers. Hence the number of good numbers is $$100 - 7 = 93$$.