A good day to everyone!
This question is an offshoot of the following MSE posts:
Can an odd perfect number be divisible by $101$?
My question is as follows:
Is there a positive ODD integer $x < 105$ for which it is known that $x$ is NOT a divisor
<p>of an odd perfect number?</p>
It is to be noted that it's currently unknown whether $3$, $5$ or any prime for that matter does divide an odd perfect number. On the other hand, it's also currently an open problem to determine if $3 \nmid N$, $5 \nmid N$, etc. holds for an odd perfect number $N$.
Postscript: Congruence-wise, we know that an odd perfect number $N$ takes one of the following forms:
$N \equiv 1 \pmod{12}$; or
<p>$N \equiv 81 \pmod{324}$; or</p> <p>$N \equiv 117 \pmod{468}$.</p>
(This is a result due to Roberts 2008.) Unfortunately, these congruences do not help much with answering this particular question.
