Let $\sigma(X)$ be the sum of the divisors of $X$, and denote the abundancy index $\sigma(X)/X$ by $I(X)$. If the equation $I(X) = r/s$ has no solution $X \in \mathbb{N}$, then $r/s$ is said to be an abundancy outlaw.
A number $Y \neq X$ is said to be a friend of $X$ if $I(Y) = I(X)$. If a number $Z$ does not have a friend, then it is said to be solitary. Greening's Theorem provides a sufficient but not necessary condition for a number to be solitary - namely, $\gcd\left(Z, \sigma(Z)\right) = 1 \implies Z$ is solitary.
Here is my first question:
(1-A) Does the Descartes number $D = 198585576189$ have a friend?
Greening's Theorem fails to establish the number's solitude, because $$\gcd\left(D, \sigma(D)\right) = \gcd(198585576189, 426027470778) = \gcd\left({3^2}\cdot{7^2}\cdot{{11}^2}\cdot{{13}^2}\cdot{{19}^2}\cdot{61},{2}\cdot{3^3}\cdot{7}\cdot{13}\cdot{{19}^2}\cdot{31}\cdot{61}\cdot{127}\right) = {3^2}\cdot{7}\cdot{13}\cdot{{19}^2}\cdot{61} = 18035199.$$
Here is a way to rephrase my first question:
(1-B) Is there a number $\overline{D} \neq 198585576189$ such that $$I(\overline{D}) = I(D) = \dfrac{{2}\cdot{3}\cdot{31}\cdot{127}}{{7}\cdot{{11}^2}\cdot{13}} = \dfrac{23622}{11011}?$$
Notice that $11011$ is a palindrome (in base-$10$). Note also that $23622$ is almost a palindrome (again, in base-$10$).
This brings me to my second question:
(2) Is the ratio $22622/11011$ an abundancy index or outlaw?