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 A326305 Dirichlet g.f.: zeta(s-1) * (1 - 2^(-s)) / zeta(s). 1
 1, 0, 2, 1, 4, 0, 6, 2, 6, 0, 10, 2, 12, 0, 8, 4, 16, 0, 18, 4, 12, 0, 22, 4, 20, 0, 18, 6, 28, 0, 30, 8, 20, 0, 24, 6, 36, 0, 24, 8, 40, 0, 42, 10, 24, 0, 46, 8, 42, 0, 32, 12, 52, 0, 40, 12, 36, 0, 58, 8, 60, 0, 36, 16, 48, 0, 66, 16, 44, 0, 70, 12, 72, 0, 40 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Moebius transform of A026741. Dirichlet convolution of A002131 with Dirichlet inverse of A000005. Dirichlet convolution of A000027 with Dirichlet inverse of A001511. LINKS FORMULA a(n) = phi(n) if n odd, phi(n) - phi(n/2) if n even, where phi = A000010. a(n) = Sum_{d|n} mu(n/d) * A026741(d). a(n) = Sum_{d|n} A007427(n/d) * A002131(d). a(n) = Sum_{d|n} A092673(n/d) * d. a(p) = p - 1, where p is odd prime. Product_{n>=1} 1 / (1 - x^n)^a(n) = g.f. for A299069. Sum_{k=1..n} a(k) ~ 9*n^2 / (4*Pi^2). - Vaclav Kotesovec, Oct 26 2019 MATHEMATICA Table[Sum[MoebiusMu[n/d] Numerator[d/2], {d, Divisors[n]}], {n, 1, 75}] a[n_] := If[OddQ[n], EulerPhi[n], EulerPhi[n] - EulerPhi[n/2]]; Table[a[n], {n, 1, 75}] PROG (MAGMA) [IsOdd(n) select EulerPhi(n) else EulerPhi(n)-EulerPhi(n div 2) : n in [1..80]]; // Marius A. Burtea, Oct 17 2019 CROSSREFS Cf. A000005, A000010, A000027, A001511, A002131, A007427, A008683, A016825 (positions of 0's), A026741, A092673, A299069. Sequence in context: A106316 A300721 A126707 * A057458 A291193 A291200 Adjacent sequences:  A326302 A326303 A326304 * A326306 A326307 A326308 KEYWORD nonn,mult AUTHOR Ilya Gutkovskiy, Oct 17 2019 STATUS approved

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Last modified October 27 17:25 EDT 2020. Contains 338035 sequences. (Running on oeis4.)