Asymmetric Numbers: Integers with Dominant Large Divisor Sum

We introduce and investigate a new class of integers called asymmetric numbers, defined by the property that the difference between the sum of their large proper divisors (greater than √n) and the sum of small proper divisors (less than √n) exceeds the number itself. We characterize structural properties, propose formal conjectures on density and asymptotic behavior, and outline computational methods for their study.