The abundance and factor-ordering conjecture for spoof odd perfect numbers

Let $n=km>1$ be a spoof odd perfect number, where $I(x)=\sigma(x)/x$ is the abundancy index. Abundance and factor-ordering conjecture. The following conditions hold:

• $I(n)>2$, so $n$ is abundant.
• If $\gcd(m,k)=1$, then

$$\sqrt{k}<m<k.$$

These predictions extend the factor-ordering discussion for spoof odd perfect numbers and are consistent with Descartes' example. The source does not provide a proof or a resolution of either assertion.