A329462 - OEIS

%I #4 Nov 15 2019 21:35:39

%S 1,1,1,2,2,1,1,2,2,3,1,2,2,2,2,3,2,2,1,5,2,1,1,2,4,4,2,3,3,5,1,3,1,3,

%T 3,4,2,2,3,6,3,4,1,2,5,3,1,3,3,8,3,6,3,4,3,4,2,4,2,7,3,4,4,4,7,4,1,5,

%U 3,7,2,4,2,6,7,3,3,9,3,8,5,5,2,7,6,4,5,3,4,14

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

%C Inverse Moebius transform of A033461.

%F G.f.: Sum_{k>=1} A033461(k) * x^k / (1 - x^k).

%F a(n) = Sum_{d|n} A033461(d).

%t nmax = 90; CoefficientList[Series[Sum[-1 + Product[(1 + x^(k j^2)), {j, 1, Floor[nmax^(1/2)] + 1}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A033461, A047966, A047968, A329439.

%K nonn

%O 1,4

%A _Ilya Gutkovskiy_, Nov 13 2019