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A308063
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Number of ordered factorizations of n into numbers with an odd number of distinct prime divisors.
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2
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1, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 5, 1, 2, 2, 8, 1, 5, 1, 5, 2, 2, 1, 12, 2, 2, 4, 5, 1, 7, 1, 16, 2, 2, 2, 14, 1, 2, 2, 12, 1, 7, 1, 5, 5, 2, 1, 28, 2, 5, 2, 5, 1, 12, 2, 12, 2, 2, 1, 21, 1, 2, 5, 32, 2, 7, 1, 5, 2, 7, 1, 37, 1, 2, 5, 5, 2, 7, 1, 28, 8, 2, 1, 21, 2, 2, 2, 12, 1, 21
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OFFSET
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1,4
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LINKS
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FORMULA
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G.f. A(x) satisfies: A(x) = x + Sum_{k>=1} A(x^A030230(k)).
a(1) = 1; a(n) = Sum_{d|n, d<n} A092248(n/d)*a(d).
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MATHEMATICA
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terms = 90; A[_] = 0; Do[A[x_] = x + Sum[Boole[OddQ[PrimeNu[k]]] A[x^k], {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]
f[n_] := f[n] = Boole[OddQ[PrimeNu[n]]]; a[n_] := If[n == 1, n, Sum[If[d < n, f[n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 90}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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