A weird number is a positive integer n such that the sum of the proper divisors of n is greater than n, but no subset of its proper divisors add up to n. What is the smallest weird number?

**The smallest weird number is 70, **which has proper divisors 1, 2, 5, 7, 10, 14, and 35. They sum to 74, which is greater that the number itself, but no subset of them sums to SEVENTY..