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%I #19 Jun 06 2021 19:22:42
%S 2,19,51,78,84,130,294,910,2223,2642,3261,4312,4973,7846,9439
%N Numbers k such that A136676(k) is prime.
%C A136676(k) = Numerator of Sum_{j=1..k} (-1)^(j+1)/j^5.
%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^5, {k,1,n} ] ]; If[ PrimeQ[f], Print[ {n,f} ] ], {n,1,130} ]
%Y Cf. A058313, A119682, A136675, A120296, A136676, A136677.
%Y Cf. A001008, A007406, A007408, A007410, A099828, A103345.
%Y Cf. A136681, A136682, A136683, A136684, A136686.
%K nonn,more
%O 1,1
%A _Alexander Adamchuk_, Jan 16 2008
%E a(7)-a(8) from _Amiram Eldar_, Mar 14 2019
%E a(9)-a(15) from _Robert Price_, Apr 16 2019
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