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Primes p such that denominator of Sum_{k=1..p-1} 1/k^7 is a seventh power.
7

%I #8 Mar 25 2020 06:51:24

%S 2,3,5,11,13,17,29,31,37,41,83,131,251,257,263,269,271,293,419,421,

%T 479,1163,1171,1181,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,

%U 3137,3163,3167,3169,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607

%N Primes p such that denominator of Sum_{k=1..p-1} 1/k^7 is a seventh power.

%H Amiram Eldar, <a href="/A127051/b127051.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^7; If[PrimeQ[i + 1], If[IntegerQ[(Denominator[su])^(1/7)], AppendTo[a, i + 1]]]]; a]; d[2000]

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

%K nonn

%O 1,1

%A _Artur Jasinski_, Jan 03 2007