The topic of odd perfect numbers likely needs no introduction.
Euler proved that a hypothetical odd perfect number $N$, if one exists, must have the so-called Eulerian form $N=q^k n^2$, where $q$ is the special prime satisfying $q \equiv k \equiv 1 \pmod 4$.
It is known that
$$q < \frac{2n^2}{D(n...