%I #24 Jun 07 2021 01:10:26
%S 2,3,4,5,6,9,20,21,29,119,132,151,351,434,457,462,572,611,930,1107,
%T 1157,1452,1515,2838,3997,5346,6463,6725,7664,10234,14168,14299
%N Numbers k such that A136675(k) is prime.
%C A136675(k) = Numerator of Sum_{j=1..k} (-1)^(j+1)/j^3.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%t Do[ f=Numerator[ Sum[ (-1)^(k+1)*1/k^3, {k,1,n} ] ]; If[ PrimeQ[f], Print[ {n,f} ] ], {n,1,151} ]
%t Flatten[Position[Numerator[Accumulate[Table[(-1)^(k+1) 1/k^3,{k,3000}]]],_?PrimeQ] ] (* _Harvey P. Dale_, Feb 12 2013 *)
%o (PARI) isok(n) = ispseudoprime(numerator(sum(k=1, n, (-1)^(k+1) / k^3))); \\ _Daniel Suteu_, Mar 15 2019
%Y Cf. A058313, A119682, A120296, A136675, A136676, A136677.
%Y Cf. A001008, A007406, A007408, A007410, A099828, A103345.
%Y Cf. A136681, A136682, A136684, A136685, A136686.
%K nonn,more
%O 1,1
%A _Alexander Adamchuk_, Jan 16 2008
%E More terms from _Harvey P. Dale_, Feb 12 2013
%E a(25)-a(28) from _Amiram Eldar_, Mar 15 2019
%E a(29)-a(32) from _Robert Price_, Apr 22 2019