Baroque conjectures

Let me address the views (guesses) on the four questions, about the perfect and baroque numbers, listed in the previous post:

• everybody believes that there are infinitely many (even) perfect numbers, because everybody believes that there are infinitely many Mersenne prime numbers p (i.e. prime numbers p such that 2^p-1 is a prime too);

• it seems to me that some (many? most?) specialists believe that there are only finitely many baroque numbers which are not perfect; some even think that all baroque non-perfect numbers are already known (no way!). Myself, I believe that there are infinitely many of them but finitely many for each baroqueness coefficient;

• nobody believes that there is any odd perfect number;

• I think that nobody believes that there is any odd baroque number; I don't either but I am not so sure :-).

I am interested in the race toward finding more baroque numbers.