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 A300672 Expansion of 1/(1 - Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k))). 1
 1, 0, 1, 1, 3, 3, 8, 10, 23, 32, 64, 98, 187, 296, 543, 891, 1595, 2660, 4694, 7924, 13854, 23556, 40940, 69939, 121122, 207490, 358517, 615292, 1061635, 1824013, 3144404, 5406257, 9314645, 16021922, 27595176, 47478950, 81757104, 140691461, 242232918, 416890645, 717712748, 1235289624 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Invert transform of A001222. LINKS N. J. A. Sloane, Transforms FORMULA G.f.: 1/(1 - Sum_{k>=2} A001222(k)*x^k). MATHEMATICA nmax = 41; CoefficientList[Series[1/(1 - Sum[Boole[PrimePowerQ[k]] x^k/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x] nmax = 41; CoefficientList[Series[1/(1 - Sum[PrimeOmega[k] x^k, {k, 2, nmax}]), {x, 0, nmax}], x] a[0] = 1; a[n_] := a[n] = Sum[PrimeOmega[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 41}] CROSSREFS Cf. A001222, A022559, A112967, A129921, A180305, A293549, A300671. Sequence in context: A237113 A293937 A291857 * A052407 A233174 A185350 Adjacent sequences:  A300669 A300670 A300671 * A300673 A300674 A300675 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Mar 11 2018 STATUS approved

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Last modified April 9 07:41 EDT 2020. Contains 333344 sequences. (Running on oeis4.)