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A359377
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a(n) = 1 if 3*n is squarefree, otherwise 0.
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9
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1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0
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OFFSET
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1
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COMMENTS
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Note the correspondences between four sequences:
^ ^
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inv inv
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v v
Here inv means that the sequences are Dirichlet Inverses of each other, and abs means taking absolute values.
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LINKS
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FORMULA
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Multiplicative with a(3^e) = 0, and for primes p <> 3, a(p^e) = 1 if e = 1, and 0 if e > 1.
Dirichlet g.f.: zeta(s)*(1-1/3^s).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 9/(2*Pi^2) = 0.455945... (A088245). (End)
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MATHEMATICA
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a[n_] := If[SquareFreeQ[3*n], 1, 0]; Array[a, 100] (* Amiram Eldar, Dec 30 2022 *)
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PROG
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(PARI) A359377(n) = issquarefree(3*n);
(PARI) A359377(n) = { my(f = factor(n)); prod(k=1, #f~, ((3!=f[k, 1])&&(1==f[k, 2]))); };
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CROSSREFS
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Characteristic function of A261034.
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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