Does this sequence finite and complete?

[Artur]

I was contribited in ONEIS following sequence of primes:
%S A127064 2, 3, 5, 17
%N A127064 Primes p such that denominator of Sum_{k=1..p-1} 1/k^2} is  
square and denominator Sum_{k=1..p-1} 1/k^3} is cube and denominator  
Sum_{k=1..p-1} 1/k^4} is fourth power and denominator Sum_{k=1..p-1}  
1/k^5} is fifth power and denominator Sum_{k=1..p-1} 1/k^6} is sixth power
%C A127064 Does this sequence finite and complete?
%Y A127064 Cf. A061002, A034602, A127029, A127042, A127043, A127044,  
A127046, A127047, A127048, A127049, A127051, A127061, A127062, A127063
%O A127064 1
%K A127064 ,nonn,
%A A127064 Artur Jasinski (grafix at csl.pl), Jan 04 2007

I'm asking: Does this sequence finite and complete?

Who can prooved these hypothesis or give countersample ?

ARTUR JASINSKI