(Note: This was cross-posted from MSE.) I posted the following reference request in MSE three (3) days ago, but was unable to elicit any responses. I am cross-posting it to MO, hoping that it is *appropriate* for this site.

I would like to request references to research done as to whether the Euler prime of an odd perfect number can also be its largest factor.

To be more specific, the Euler prime $q$ of an odd perfect number $N$ is the *sole*
prime factor that occurs to an (odd) exponent $k \equiv 1 \pmod 4$. That is, we can write this odd perfect number in the form $N = {q^k}{n^2}$, where $\gcd(q, n) = 1$.

In an e-mail, it was communicated to me by Douglas Iannucci that his adviser, Peter Hagis Jr., considered this possibility.

I was wondering if anybody here knows of any partial results in this direction.

Thank you!

[Added Feb 8 2015] We do know that the Euler prime $q$ is not the smallest prime factor of an odd perfect number $N = {q^k}{n^2}$. To see why, it suffices to consider:

$$q + 1 = \sigma(q) \mid \sigma(q^k) \mid 2N.$$

good reasonfor your very quick downvote? =) $\endgroup$ – Jose Arnaldo Bebita-Dris Feb 11 '15 at 19:05