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%I #16 Mar 25 2020 06:50:29
%S 2,3,5,7,17,19,41,43,47,97,127,191,193,197,199,211,223,227,229,739,
%T 743,751,757,761,769,773,787,797,809,811,991,997,1009,1013,1187,1193,
%U 1201,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3613,3617,3623,3631
%N Primes p such that denominator of Sum_{k=1..p-1} 1/k^6 is a sixth power.
%H Amiram Eldar, <a href="/A127049/b127049.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^6; If[PrimeQ[i + 1] && IntegerQ[(Denominator[su])^(1/6)], AppendTo[a, i + 1]]]; a]; d[2000]
%t Select[Prime[Range[600]],IntegerQ[Surd[Denominator[Sum[1/k^6,{k,#-1}]], 6]]&] (* _Harvey P. Dale_, Aug 04 2019 *)
%Y Cf. A061002, A034602, A127029, A127042, A127043, A127044, A127046, A127047, A127048, A127049, A127051.
%K nonn
%O 1,1
%A _Artur Jasinski_, Jan 03 2007, Jan 04 2007
%E Edited by _N. J. A. Sloane_, Jul 03 2008 at the suggestion of _R. J. Mathar_