(Note: This was cross-posted from [MSE](https://math.stackexchange.com/questions/1138363).) 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](http://en.wikipedia.org/wiki/Perfect_number#Odd_perfect_numbers) 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](http://genealogy.math.ndsu.nodak.edu/id.php?id=26955) that his adviser, [Peter Hagis Jr.](http://genealogy.math.ndsu.nodak.edu/id.php?id=26966), 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:


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



Reference request: Research done on whether the Euler prime can be the largest factor of an odd perfect number
[This paper](http://www.math.missouri.edu/~bbanks/papers/2008_Descartes_Final.pdf) by Bill Banks et al. studies spoof OPN's similar to Descartes' spoof, and of course in Descartes' spoof the "quasi" Euler prime is the biggest prime.


