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 A359378 Dirichlet inverse of A359377, where A359377(n) = 1 if 3*n is squarefree, otherwise 0. 9
 1, -1, 0, 1, -1, 0, -1, -1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, -1, 0, 1, -1, 0, 1, 1, 0, -1, -1, 0, -1, -1, 0, 1, 1, 0, -1, 1, 0, 1, -1, 0, -1, -1, 0, 1, -1, 0, 1, -1, 0, -1, -1, 0, 1, 1, 0, 1, -1, 0, -1, 1, 0, 1, 1, 0, -1, -1, 0, -1, -1, 0, -1, 1, 0, -1, 1, 0, -1, -1, 0, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, -1, 0, 1, 1, 0, -1, -1, 0, 1, -1, 0, -1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS Note the correspondences between four sequences: A156277 --- abs ---> A359377 ^ ^ | | inv inv | | v v A011655 <--- abs --- A359378 (this sequence) Here inv means that the sequences are Dirichlet Inverses of each other, and abs means taking absolute values. LINKS Antti Karttunen, Table of n, a(n) for n = 1..100000 FORMULA a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d 3. a(n) = A359170(n) - A359172(n). For all n >= 1, a(A001651(n)) = A008836(A001651(n)). Dirichlet g.f.: 3^s/((3^s-1)*zeta(s)). - Amiram Eldar, Jan 03 2023 MATHEMATICA f[p_, e_] := (-1)^e; f[3, e_] := 0; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Dec 30 2022 *) PROG (PARI) A359378(n) = { my(f = factor(n)); prod(k=1, #f~, (3!=f[k, 1])*((-1)^f[k, 2])); }; CROSSREFS Cf. A001651, A008836, A011655 (absolute values), A156277 (Dirichlet inverse of the absolute values), A359377 (Dirichlet inverse). Cf. A008585 (after its initial term gives the positions of 0's), A359171 (of positive terms), A359381 (of negative terms), A359170, A359172. Cf. also A166698, A358839. Sequence in context: A049347 A010892 A091338 * A016345 A016148 A016333 Adjacent sequences: A359375 A359376 A359377 * A359379 A359380 A359381 KEYWORD sign,mult AUTHOR Antti Karttunen, Dec 29 2022 STATUS approved

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Last modified October 3 16:08 EDT 2023. Contains 365868 sequences. (Running on oeis4.)