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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 Robert Israel, Table of n, a(n) for n = 0..5456 Eric Weisstein's World of Mathematics, Squarefree Index entries for sequences related to compositions 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 Cf. A005117, A008683, A073576, A144338, A280127, A280194. Sequence in context: A130780 A174524 A143592 * A333526 A097307 A323435 Adjacent sequences: A280194 A280195 A280196 * A280198 A280199 A280200 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.)