A127046 Primes p such that denominator of Sum_{k=1..p-1} 1/k^3 is a cube.

2, 3, 5, 11, 13, 17, 29, 31, 37, 41, 83, 89, 97, 137, 139, 293, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103

Offset: 1

Author

Artur Jasinski, Jan 03 2007

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A061002, A034602, A127029, A127042.

Programs

Mathematica

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]
Select[Prime[Range[200]], IntegerQ[Surd[Denominator[Sum[1/k^3, {k,#-1}]], 3]]&] (* Harvey P. Dale, Mar 13 2013 *)