%I #8 Jul 02 2021 16:43:00
%S 1,0,1,-1,0,-1,-1,-1,-2,0,-3,1,-4,3,-5,5,-5,6,-6,10,-7,11,-6,15,-7,14,
%T -7,19,-5,17,-6,23,-7,18,-4,24,-2,16,-3,23,1,13,0,17,-1,7,7,14,6,-7,7,
%U 0,12,-13,11,-14,15,-33,21,-27,20,-57,19,-50,29,-73,34,-79,33,-96
%N a(1) = 1, a(2) = 0; a(n+2) = Sum_{d|n} mu(n/d) * a(d).
%F G.f. A(x) satisfies: A(x) = x + x^2 * Sum_{k>=1} mu(k) * A(x^k).
%t a[1] = 1; a[2] = 0; a[n_] := a[n] = Sum[MoebiusMu[(n - 2)/d] a[d], {d, Divisors[n - 2]}]; Table[a[n], {n, 1, 70}]
%t nmax = 70; A[_] = 0; Do[A[x_] = x + x^2 Sum[MoebiusMu[k] A[x^k], {k, 1, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%Y Cf. A007439, A007554, A008683, A318583, A345138, A345141.
%K sign
%O 1,9
%A _Ilya Gutkovskiy_, Jul 01 2021