A number is said to be "weird" if it is abundant without being the sum of any set of its own divisors.

An example of this is 70 because the sum of its divisors is 1+2+5+7+10+14+35 = 74. As you can see 74 is greater than 70 so it is "abundant" and in addition, no set of divisors when you add them up will give you 70. Therefore 70 is a "weird" number

Problem: Find all of the weird numbers below 10,000 (Hint: they are all even)

HISTORICAL NOTE: Erdos, the Hungarian number theorist once offered $10 in 1971 for an example of an odd weird number or $25 dollars for proof that none exists.

Extension: Now I realize that Erdos passed away earlier this year so technically the bet can no longer be offered, but for extension's sake, is there indeed an odd weird number? If not, prove that none exist.