WEIRD NUMBERS

Weird Number-

Weird...

a weird number is a natral number that is abundant but not semipefect. The smallest weird number is 70. Its proper divisors are 1, 2, 5, 7, 10, 14, and 35; these sum to 74. So the prime factorization to weird numbers is it's factors all added up to get the number. It has been shown that an infinite number of weird numbers exist.

Weirder...

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