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A329434 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*(2*j - 1)))). 0
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, 28, 21, 32, 29, 32, 32, 47, 36, 44, 46, 60, 50, 67, 58, 75, 77, 82, 79, 112, 95, 114, 114, 134, 126, 157, 148, 181, 176, 196, 193, 248, 224, 257, 268, 308, 299 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Inverse Moebius transform of A000700.
LINKS
FORMULA
G.f.: Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 + (-1)^j * x^(k*j))).
G.f.: Sum_{k>=1} A000700(k) * x^k / (1 - x^k).
a(n) = Sum_{d|n} A000700(d).
MATHEMATICA
nmax = 65; CoefficientList[Series[Sum[-1 + Product[(1 + x^(k (2 j - 1))), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest
CROSSREFS
Sequence in context: A300066 A286545 A046798 * A157231 A332888 A258596
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 13 2019
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)