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A280197 Expansion of 1/(1 - Sum_{k>=2} mu(k)^2*x^k), where mu(k) is the Moebius function (A008683). 1
1, 0, 1, 1, 1, 3, 3, 6, 8, 12, 20, 28, 45, 68, 102, 159, 238, 367, 557, 849, 1298, 1973, 3015, 4592, 7002, 10679, 16276, 24822, 37841, 57696, 87971, 134119, 204497, 311783, 475370, 724786, 1105053, 1684853, 2568837, 3916642, 5971587, 9104711, 13881698, 21165024, 32269721, 49200718, 75014949, 114373158, 174381511 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
Number of compositions (ordered partitions) into squarefree parts > 1 (A144338).
LINKS
Eric Weisstein's World of Mathematics, Squarefree
FORMULA
G.f.: 1/(1 - Sum_{k>=2} mu(k)^2*x^k).
EXAMPLE
a(5) = 3 because we have [5], [3, 2] and [2, 3].
MAPLE
N:= 100: # for a(0)..a(N)
g:= 1/(1-add(numtheory:-mobius(k)^2*x^k, k=2..N)):
S:= series(g, x, N+1):
seq(coeff(S, x, j), j=0..N); # Robert Israel, Dec 29 2016
MATHEMATICA
nmax = 48; CoefficientList[Series[1/(1 - Sum[MoebiusMu[k]^2 x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
CROSSREFS
Sequence in context: A130780 A174524 A143592 * A333526 A097307 A323435
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 28 2016
STATUS
approved

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Last modified February 26 02:20 EST 2024. Contains 370335 sequences. (Running on oeis4.)