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%I #7 Apr 16 2021 15:42:06
%S 4,-6,24,-66,208,-676,2344,-8226,29144,-104760,381304,-1398476,
%T 5162224,-19172796,71582944,-268439586,1010580544,-3817734596,
%U 14467258264,-54975633768,209430787824,-799644629556,3059510616424,-11728124734476,45035996273872,-173215367702376,667199944815064
%N a(n) = -(1/n) * Sum_{d|n} phi(n/d) * (-4)^d.
%F G.f.: Sum_{k>=1} phi(k) * log(1 + 4*x^k) / k.
%F a(n) = -(1/n) * Sum_{k=1..n} (-4)^gcd(n,k).
%F Product_{n>=1} 1 / (1 - x^n)^a(n) = g.f. for A261568.
%t Table[-(1/n) Sum[EulerPhi[n/d] (-4)^d, {d, Divisors[n]}], {n, 1, 27}]
%t nmax = 27; CoefficientList[Series[Sum[EulerPhi[k] Log[1 + 4 x^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%Y Cf. A000010, A001868, A038065, A074763, A261568, A343465, A343467.
%K sign
%O 1,1
%A _Ilya Gutkovskiy_, Apr 16 2021
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