%I #8 Mar 25 2020 06:51:18
%S 2,3,5,11,13,17,37,41,53,83,127,131,137,139,149,151,389,397,401,409,
%T 419,421,431,433,439,443,733,739,743,751,757,761,769,773,787,797,809,
%U 811,853,857,859,863,877,881,883,887,929,967,1091,1093,1097,1103,1109,1151
%N Primes p such that denominator of Sum_{k=1..p-1} 1/k^5 is a fifth power.
%H Amiram Eldar, <a href="/A127048/b127048.txt">Table of n, a(n) for n = 1..10000</a>
%t d[n_] := Module[{}, su = 0; a = {}; For[i = 1, i <= n, i++, su = su + 1/ i^5; If[PrimeQ[i + 1], If[IntegerQ[(Denominator[su])^(1/5)], AppendTo[a, i + 1]]]]; a]; d[2000]
%Y Cf. A061002, A034602, A127029, A127042, A127046, A127047.
%K nonn
%O 1,1
%A _Artur Jasinski_, Jan 03 2007