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A353627
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a(n) = 1 if the odd part of n is squarefree, otherwise 0.
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21
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1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0
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OFFSET
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1
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COMMENTS
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Sequence gives the absolute values of A209635. See discussion there.
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.
(End)
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LINKS
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FORMULA
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Multiplicative with a(2^e) = 1, and for odd primes p, a(p^e) = 1 if e = 1 and 0 if e > 1.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 8/Pi^2 (A217739). - Amiram Eldar, Jul 23 2022
Dirichlet g.f.: zeta(s)/(zeta(2*s)*(1-1/4^s)). - Amiram Eldar, Jan 01 2023
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MATHEMATICA
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a[n_] := If[SquareFreeQ[n/2^IntegerExponent[n, 2]], 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 23 2022 *)
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PROG
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(PARI) A353627(n) = issquarefree(n>>valuation(n, 2));
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CROSSREFS
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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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