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A329462
Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*j^2))).
1
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, 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, 3, 7, 2, 4, 2, 6, 7, 3, 3, 9, 3, 8, 5, 5, 2, 7, 6, 4, 5, 3, 4, 14
OFFSET
1,4
COMMENTS
Inverse Moebius transform of A033461.
FORMULA
G.f.: Sum_{k>=1} A033461(k) * x^k / (1 - x^k).
a(n) = Sum_{d|n} A033461(d).
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 13 2019
STATUS
approved