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

2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 53, 67, 71, 73, 97, 101, 103, 107, 109, 127, 131, 197, 199, 211, 223, 227, 229, 233, 293, 367, 373, 379, 383, 389, 397, 401, 439, 443, 449, 457, 461, 463, 557, 563, 569, 571, 577, 877, 881, 883, 967, 971, 977, 983, 991, 997

Offset: 1

Author

Artur Jasinski, Jan 03 2007

Keywords

• nonn
• look

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..665 from Robert Israel)

Crossrefs

Cf. A061002, A034602, A127029, A127042, A127046.

Programs

Maple

S:= 0: R:= NULL: count:= 0:
for k from 1 while count < 100 do
  S:= S + 1/k^4;
  if isprime(k+1) and surd(denom(S),4)::integer then R:= R,k+1; count:= count+1 fi
od:
R; # Robert Israel, Oct 25 2019

Mathematica

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]
Select[Flatten[Position[Denominator[Accumulate[1/Range[1000]^4]],?(IntegerQ[ Surd[ #,4]]&)]],PrimeQ] (* _Harvey P. Dale, Feb 08 2015 *)