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%I #12 Jan 03 2024 07:18:28
%S 2,3,5,11,13,17,29,31,37,41,83,89,97,137,139,293,373,379,383,389,397,
%T 401,409,419,421,431,433,439,443,449,457,461,463,467,479,1009,1013,
%U 1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103
%N Primes p such that denominator of Sum_{k=1..p-1} 1/k^3 is a cube.
%H Chai Wah Wu, <a href="/A127046/b127046.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^3; If[PrimeQ[i + 1], If[IntegerQ[(Denominator[su])^(1/3)], AppendTo[a, i + 1]]]]; a]; d[2000]
%t Select[Prime[Range[200]], IntegerQ[Surd[Denominator[Sum[1/k^3, {k,#-1}]], 3]]&] (* _Harvey P. Dale_, Mar 13 2013 *)
%Y Cf. A061002, A034602, A127029, A127042.
%K nonn
%O 1,1
%A _Artur Jasinski_, Jan 03 2007