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A127047 Primes p such that denominator of Sum_{k=1..p-1} 1/k^4 is a fourth power.

%I A127047 #17 Mar 25 2020 06:51:12
%S A127047 2,3,5,7,11,13,17,19,29,31,53,67,71,73,97,101,103,107,109,127,131,197,
%T A127047 199,211,223,227,229,233,293,367,373,379,383,389,397,401,439,443,449,
%U A127047 457,461,463,557,563,569,571,577,877,881,883,967,971,977,983,991,997
%N A127047 Primes p such that denominator of Sum_{k=1..p-1} 1/k^4 is a fourth power.
%H A127047 Amiram Eldar, <a href="/A127047/b127047.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..665 from Robert Israel)
%p A127047 S:= 0: R:= NULL: count:= 0:
%p A127047 for k from 1 while count < 100 do
%p A127047   S:= S + 1/k^4;
%p A127047   if isprime(k+1) and surd(denom(S),4)::integer then R:= R,k+1; count:= count+1 fi
%p A127047 od:
%p A127047 R; # _Robert Israel_, Oct 25 2019
%t A127047 d[n_] := Module[{}, su = 0; a = {}; For[i = 1, i <= n, i++, su = su + 1/ i^4; If[PrimeQ[i + 1], If[IntegerQ[(Denominator[su])^(1/4)], AppendTo[a, i + 1]]]]; a]; d[10000]
%t A127047 Select[Flatten[Position[Denominator[Accumulate[1/Range[1000]^4]],_?(IntegerQ[ Surd[ #,4]]&)]],PrimeQ] (* _Harvey P. Dale_, Feb 08 2015 *)
%Y A127047 Cf. A061002, A034602, A127029, A127042, A127046.
%K A127047 nonn,look
%O A127047 1,1
%A A127047 _Artur Jasinski_, Jan 03 2007