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A359590
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Absolute values of A355690, where A355690 is the Dirichlet inverse of the characteristic function of numbers not congruent to 2 mod 4.
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8
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1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1
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OFFSET
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1
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LINKS
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FORMULA
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Multiplicative with a(2^e) = 1 if e mod 3 == 0 or 2, otherwise 0, and for odd primes p, a(p^e) = 1 if e = 1, otherwise 0.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 40/(7*Pi^2) = 0.578978... .
Dirichlet g.f.: (zeta(s)/zeta(2*s))*(16^s+4^s)/((2^s+1)*(8^s-1)). (End)
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MATHEMATICA
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f[p_, e_] := If[e == 1, 1, 0]; f[2, e_] := If[Mod[e, 3] == 1, 0, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 11 2023 *)
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PROG
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(PARI) A359590(n) = { my(f = factor(n)); prod(k=1, #f~, if(2==f[k, 1], !(1==(f[k, 2]%3)), (1==f[k, 2]))); };
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CROSSREFS
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Parity of A355690, and also its absolute values.
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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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