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%I #9 Jan 03 2024 07:18:16
%S 2,3,5,11,13,17,29,31,37,97,127,131,251,257,263,293,431,433,439,443,
%T 449,457,461,463,467,3137,3163,3167,3169,3181,3187,3191,3203,3209,
%U 3217,3221,3229,3251,3253,3257,3259,3271,3797,3803,3821,3823,3833,3907,3911,3917
%N Primes p such that denominator of Sum_{k=1..p-1} 1/k^9 is a 9th power.
%H Chai Wah Wu, <a href="/A127045/b127045.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^9; If[PrimeQ[i + 1], If[IntegerQ[(Denominator[su])^(1/9)], AppendTo[a, i + 1]]]]; a] d[2000]
%t Select[Flatten[Position[Denominator[Accumulate[1/Range[4000]^9]],_?(IntegerQ[ Surd[ #,9]]&)]]+1,PrimeQ] (* _Harvey P. Dale_, Aug 06 2022 *)
%Y Cf. A061002, A034602, A127029, A127042, A127043, A127044, A127046, A127047, A127048, A127049, A127051.
%K nonn
%O 1,1
%A _Artur Jasinski_, Jan 04 2007