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 A363551 Möbius function of rank 3: a(n) = lambda(n) = A008836(n) if n is cubefree and 0 otherwise. 4
 1, -1, -1, 1, -1, 1, -1, 0, 1, 1, -1, -1, -1, 1, 1, 0, -1, -1, -1, -1, 1, 1, -1, 0, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, -1, 1, 1, 0, -1, -1, -1, -1, -1, 1, -1, 0, 1, -1, 1, -1, -1, 0, 1, 0, 1, 1, -1, 1, -1, 1, -1, 0, 1, -1, -1, -1, 1, -1, -1, 0, -1, 1, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS First differs from A307420 at n = 63. The Möbius function of rank 2 is the Möbius function (A008683). Dirichlet inverse of A299406. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Masato Kobayashi, Möbius functions of higher rank and Dirichlet series, arXiv:2108.01822 [math.NT], 2021. FORMULA a(n) = A008836(n) * A212793(n). abs(a(n)) = A212793(n). Multiplicative with a(p^e) = (-1)^e if e <= 2, and 0 otherwise. Dirichlet g.f.: Product_{p prime} (1 - 1/p^s + 1/p^(2*s)) = zeta(2*s)*zeta(3*s)/(zeta(s)*zeta(6*s)). MATHEMATICA f[p_, e_] := If[e < 3, (-1)^e, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] PROG (PARI) f(e) = if(e < 3, (-1)^e, 0); a(n) = vecprod(apply(f, factor(n)[, 2])); CROSSREFS Cf. A008683, A008836, A046099, A004709, A212793, A299406, A307420, A363552, A363553. Other generalizations of the Möbius function: A053864, A053865, A053981, A189021, A189022, A189023. Sequence in context: A119981 A115789 A359471 * A053864 A189021 A212793 Adjacent sequences: A363548 A363549 A363550 * A363552 A363553 A363554 KEYWORD sign,mult,easy AUTHOR Amiram Eldar, Jun 10 2023 STATUS approved

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Last modified April 14 13:30 EDT 2024. Contains 371661 sequences. (Running on oeis4.)