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%I #4 Nov 15 2019 21:35:50
%S 1,1,2,2,1,3,2,2,3,3,2,4,2,3,3,4,2,5,3,5,5,4,1,6,4,3,4,7,3,7,5,7,3,5,
%T 5,8,5,6,6,8,3,10,4,7,8,7,5,10,7,10,5,10,6,9,9,13,7,8,6,14,7,10,10,14,
%U 9,12,9,12,7,17,8,14,10,14,12,17,12,12,10,20
%N Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*j*(j + 1)/2))).
%C Inverse Moebius transform of A024940.
%F G.f.: Sum_{k>=1} A024940(k) * x^k / (1 - x^k).
%F a(n) = Sum_{d|n} A024940(d).
%t nmax = 80; CoefficientList[Series[Sum[-1 + Product[(1 + x^(k j (j + 1)/2)), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%Y Cf. A024940, A047966, A047968, A329462, A329465.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, Nov 13 2019
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