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%I #12 Apr 30 2019 03:15:18
%S 1,1,0,1,-1,0,0,1,-2,-1,0,1,0,1,1,1,-3,-2,0,1,2,3,3,4,1,1,1,0,-2,-1,
%T -2,-1,-6,-5,-2,-2,2,3,3,4,3,4,3,4,0,-1,-4,-3,-11,-10,-11,-13,-15,-14,
%U -15,-15,-18,-17,-15,-14,-11,-10,-8,-7,-11,-11,-2,-1,6,10,13,14,21,22,20
%N a(1) = 1; a(n+1) = Sum_{d|n} (-1)^(n/d+1)*a(d).
%F G.f.: x * (1 + Sum_{n>=1} a(n)*x^n/(1 + x^n)).
%F L.g.f.: log(Product_{n>=1} (1 + x^n)^(a(n)/n)) = Sum_{n>=1} a(n+1)*x^n/n.
%p with(numtheory): P:=proc(q) local a,d,n; a:=[1]:
%p for n from 1 to q do a:=[op(a),add((-1)^(n/d+1)*a[d],d=divisors(n))]:
%p od; op(a); end: P(74); # _Paolo P. Lava_, Apr 30 2019
%t a[n_] := a[n] = Sum[(-1)^((n - 1)/d + 1) a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 75}]
%t a[n_] := a[n] = SeriesCoefficient[x (1 + Sum[a[k] x^k/(1 + x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 75}]
%Y Cf. A003238, A281487, A307777, A307778, A307779.
%K sign
%O 1,9
%A _Ilya Gutkovskiy_, Apr 28 2019
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