when is the sum of divisors[n] prime?

[Wouter Meeussen]

hi,
interesting stuff (to an amateur like me).

it=Select[Range[10000],PrimeQ[DivisorSigma[1,#]]&]
Out={2,4,9,16,25,64,289,729,1681,2401,3481,4096,5041,7921}

all these integers have the form:
p1^(p2-1) with p1 and p2 prime.

for p1=2, the p2 are the Mersenne primes-1 :
DivisorSigma[1,2^(m-1)] = 1+2+2^2+2^3+..+2^(m-1)=2^m -1 == prime by def. 


I got stuck where I need to show that
"Sum[p^i,{i,0,n}] factors if n is non-prime"
Does rhat follow from Fermat's little one?