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A329465
Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 - x^(k*j*(j + 1)/2))).
1
1, 2, 3, 4, 3, 8, 5, 8, 9, 11, 8, 20, 12, 17, 20, 25, 18, 36, 25, 38, 39, 44, 37, 68, 51, 63, 69, 85, 69, 113, 90, 117, 117, 136, 128, 189, 154, 185, 195, 239, 206, 288, 253, 308, 321, 358, 333, 457, 406, 476, 485, 566, 521, 671, 629, 734, 737, 833, 794, 1019
OFFSET
1,2
COMMENTS
Inverse Moebius transform of A007294.
FORMULA
G.f.: Sum_{k>=1} A007294(k) * x^k / (1 - x^k).
a(n) = Sum_{d|n} A007294(d).
MATHEMATICA
nmax = 60; CoefficientList[Series[Sum[-1 + Product[1/(1 - x^(k j (j + 1)/2)), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 13 2019
STATUS
approved