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%I #4 Sep 07 2018 04:46:34
%S 1,3,6,6,8,18,10,10,24,24,14,36,16,30,48,15,20,72,22,48,60,42,26,60,
%T 46,48,82,60,32,144,34,21,84,60,80,144,40,66,96,80,44,180,46,84,192,
%U 78,50,90,76,138,120,96,56,246,112,100,132,96,62,288,64,102,240,28,128,252,70,120,156,240
%N a(n) = Sum_{d|n} (-1)^(n/d+1) * Sum_{j|d} sigma(j), where sigma(j) = sum of divisors of j (A000203).
%F G.f.: Sum_{k>=1} A007429(k)*x^k/(1 + x^k).
%F L.g.f.: log(Product_{k>=1} (1 + x^k)^(A007429(k)/k)) = Sum_{n>=1} a(n)*x^n/n.
%t Table[Sum[(-1)^(n/d + 1) Sum[DivisorSigma[1, j], {j, Divisors[d]}], {d, Divisors[n]}], {n, 70}]
%t nmax = 70; Rest[CoefficientList[Series[Sum[DivisorSum[k, DivisorSigma[1, #] &] x^k/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]]
%t nmax = 70; Rest[CoefficientList[Series[Log[Product[(1 + x^k)^(DivisorSum[k, DivisorSigma[1, #] &]/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]]
%Y Cf. A000203, A007429, A007430, A288417, A318768.
%K nonn,mult
%O 1,2
%A _Ilya Gutkovskiy_, Sep 04 2018
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