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
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
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.