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 A018243 Inverse Euler transform of A000931. 1
 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 7, 8, 11, 13, 17, 21, 28, 34, 45, 56, 73, 92, 120, 151, 197, 250, 324, 414, 537, 687, 892, 1145, 1484, 1911, 2479, 3196, 4148, 5359, 6954, 9000, 11687, 15140, 19672, 25516, 33166, 43065, 56010, 72784, 94716, 123185, 160380, 208740, 271913, 354123, 461529, 601436, 784209, 1022505, 1333856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 LINKS Joerg Arndt, Table of n, a(n) for n = 1..1000 D. J. Broadhurst and D. Kreimer, Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops, Phys. Lett. B 393, No.3-4, 403-412 (1997). N. J. A. Sloane, Transforms FORMULA a(n) = A113788(n) unless n=2. - Michael Somos, Apr 06 2012 Reciprocal of g.f. of A000931 = (1 - x^2 - x^3) / (1 - x^2) = 1 - x^3 - x^5 - x^7 - x^9 - ... = Product_{k>0} (1 - x^k)^a(n). - Michael Somos, Jul 17 2012 a(n) ~ A060006^n / n. - Vaclav Kotesovec, Oct 09 2019 EXAMPLE x^3 + x^5 + x^7 + x^8 + x^9 + x^10 + 2*x^11 + 2*x^12 + 3*x^13 + 3*x^14 + ... MATHEMATICA a[n_] := (1/n)*Sum[ MoebiusMu[n/d]*Floor[ Re[ N[ RootSum[ -1-#+#^3&, #^d& ]]]] , {d, Divisors[n]}]; a[2]=0; Table[a[n], {n, 1, 65}] (* Jean-François Alcover, Oct 05 2012, after Michael Somos *) PROG (Sage) z = PowerSeriesRing(ZZ, 'z').gen().O(30) r = (1 - (z**2 + z**3))/(1 - z**2) F = -z*r.derivative()/r [sum(moebius(n//d)*F[d] for d in divisors(n))//n for n in range(1, 24)] # F. Chapoton, Apr 25 2020 CROSSREFS Cf. A000931, A113788. Sequence in context: A035575 A036816 A113788 * A127207 A173513 A147663 Adjacent sequences:  A018240 A018241 A018242 * A018244 A018245 A018246 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from Joerg Arndt, Jul 18 2012 STATUS approved

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Last modified August 12 17:17 EDT 2020. Contains 336439 sequences. (Running on oeis4.)