Not Quite Perfect

I forgot to mention semi-perfect numbers. These are numbers for which you can find some subset of its divisors (not including the number itself) that sums to the number itself. For example, even though 12 is not perfect (its divisors, if you recall, are 1, 2, 3, 4 and 6) if we use only 6, 4 and 2, we can get a sum of 12. So, 12 is semi-perfect because some of its divisors add up to it.

Now, only an abundant number can be semi-perfect, since a deficient number doesn't have enough divisors to add up to itself when you take them ALL into account.

And as it turns out, it is rather rare for an abundant number NOT to be semi-perfect. These rarities are called wierd numbers. So 70, for instance, is considered wierd because no subset of its divisors sums to 70, even though 70 is an abundant number. Test it out!