Eureka Moment #2: A Short Proof for Sorli's Conjecture on Odd Perfect Numbers (Also available via arXiv at http://arxiv.org/abs/1308.2156) - This paper contains a simple (and short) proof for Descartes' / Frenicle's / Sorli's conjecture on odd perfect numbers.
Together, these will then imply the conjecture q^k < n from this
M. Sc. thesis.
Euclid-Euler Heuristics for (Odd) Perfect Numbers
New Results for Sorli's Conjecture on Odd Perfect Numbers
The Abundancy Index of Divisors of Odd Perfect Numbers - Part II
The Abundancy Index of Divisors of Odd Perfect Numbers
Solving the Odd Perfect Number Problem: Some Old and New Approaches
OEIS sequence A228059 by Tony D. Noe, Aug 14 2013
Math Questions in MSE and MO:
On odd perfect numbers given in the Eulerian formhttp://math.stackexchange.com/questions/548528