# Do any odd weird numbers exist?

SHAIK AASIF AHAMED
7 years ago

Hello student,

Weird numbers are natural numbers that are abundant but not semiperfect. For example, 70 is the lowest weird number, because its set of proper divisors {1,2,5,7,10,14,35} sum to 74, but no subset of its set of proper divisors sum to the number 70, and 70 is the smallest number to meet such conditions. The first few weird numbers are 70, 836, 4030, and 5830 and so on.In this small sampling of weird numbers, one can see that they are all even. Thus, the following question could be asked: Do any odd weird numbers exist? This is an easy question to ask, but far from easy to answer. However, other basic properties can be described with more ease. For instance, mathematicians have proven that there are infinitely many weird numbers. Also, if an odd weird number does exist, then it must be greater than $4 X 10^9$.

Thanks and Regards

Shaik Aasif