On some properties of the Euler's factor of certain odd perfect numbers

Let n=π^α3^2βQ^2β be an odd positive integer, with π prime, π≡α≡1 (mod 4), Q squarefree, (Q,π)=(Q,3)=1. It is shown that: if n is perfect, then σ(π^α)≡0. Some corollaries concerning the Euler's factor of odd perfect numbers of the above mentioned form, if any, are deduced.