%I #4 Nov 13 2019 15:09:13

%S 1,1,2,2,2,3,2,4,4,4,3,7,4,5,7,9,6,10,7,12,11,11,10,20,14,16,18,22,18,

%T 28,21,32,29,32,32,47,36,44,46,60,50,67,58,75,77,82,79,112,95,114,114,

%U 134,126,157,148,181,176,196,193,248,224,257,268,308,299

%N Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*(2*j - 1)))).

%C Inverse Moebius transform of A000700.

%F G.f.: Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 + (-1)^j * x^(k*j))).

%F G.f.: Sum_{k>=1} A000700(k) * x^k / (1 - x^k).

%F a(n) = Sum_{d|n} A000700(d).

%t nmax = 65; CoefficientList[Series[Sum[-1 + Product[(1 + x^(k (2 j - 1))), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A000700, A047966, A047968.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Nov 13 2019