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Primes p such that denominator of Sum_{k=1..p-1} 1/k^8 is an eighth power.
1

%I #8 Mar 25 2020 06:51:29

%S 2,3,5,7,11,13,17,19,29,31,37,41,53,67,71,73,97,101,127,131,197,199,

%T 211,251,367,373,379,773,787,797,809,811,1373,1433,1439,2027,2707,

%U 2711,2713,2719,2729,2731,2741,2749,2753,3181,3187,3191,3203,3209,3217,3221,3229

%N Primes p such that denominator of Sum_{k=1..p-1} 1/k^8 is an eighth power.

%H Amiram Eldar, <a href="/A127052/b127052.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^8; If[PrimeQ[i + 1], If[IntegerQ[(Denominator[su])^(1/8)], AppendTo[a, i + 1]]]]; a]; d[2000]

%Y Cf. A061002, A034602, A127029, A127042, A127046, A127047, A127048, A127051.

%K nonn

%O 1,1

%A _Artur Jasinski_, Jan 03 2007