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%I
%S 1,7,197,1549,195353,194353,66879079,533875007,14436577189,
%T 14420574181,19209787242911,19197460851911,42198121495296467,
%U 6025866788581781,6027847576222613,48209723660000029,236907853607882606477
%N Numerator of Sum (-1)^(k+1)*1/k^3, k = 1..n.
%C a(n) is prime for n = {2,3,4,5,6,9,20,21,29,119,132,151,...} = A136683.
%H Eric Weisstein, The World of Mathematics: <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%t Table[ Numerator[ Sum[ (-1)^(k+1)*1/k^3, {k,1,n} ] ], {n,1,50} ]
%t Numerator[Accumulate[Table[(-1)^(k+1) 1/k^3,{k,50}]]] (* _Harvey P. Dale_, Feb 12 2013 *)
%Y Cf. A058313, A119682, A120296, A136676, A136677. Cf. A001008, A007406, A007408, A007410, A099828, A103345. Cf. A136681, A136682, A136683, A136684, A136685, A136686.
%K frac,nonn
%O 1,2
%A _Alexander Adamchuk_, Jan 16 2008
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