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%I #13 Jul 29 2023 10:37:14
%S 1,-2,3,-3,5,-6,8,-10,9,-9,11,-9,14,-16,15,-19,17,-18,20,-17,24,-21,
%T 23,-30,26,-28,27,-24,29,-27,32,-42,33,-33,40,-27,38,-40,42,-53,41,
%U -48,44,-35,45,-45,47,-57,57,-47,51,-42,53,-54,56,-80,60,-57,59,-51,62,-64,72,-83,70,-63,68,-53,69,-72
%N Expansion of Sum_{k>=0} x^(3*k+1) / (1 + x^(3*k+1))^2.
%H Seiichi Manyama, <a href="/A364232/b364232.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Sum_{d|n, n/d==1 (mod 3)} (-1)^(d+1) * d.
%t nmax = 70; CoefficientList[Series[Sum[x^(3 k + 1)/(1 + x^(3 k + 1))^2, {k, 0, nmax}], {x, 0, nmax}], x] // Rest
%t Table[DivisorSum[n, (-1)^(# + 1) # &, MemberQ[{1}, Mod[n/#, 3]] &], {n, 1, 70}]
%Y Cf. A002129, A186690, A326399, A364012, A364204, A364235.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, Jul 14 2023
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