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 A007432 Moebius transform applied thrice to natural numbers. (Formerly M0031) 2
 1, -1, 0, 1, 2, 0, 4, 1, 3, -2, 8, 0, 10, -4, 0, 2, 14, -3, 16, 2, 0, -8, 20, 0, 13, -10, 8, 4, 26, 0, 28, 4, 0, -14, 8, 3, 34, -16, 0, 2, 38, 0, 40, 8, 6, -20, 44, 0, 31, -13, 0, 10, 50, -8, 16, 4, 0, -26, 56, 0, 58, -28, 12, 8, 20, 0, 64, 14 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n=1..1000 M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version] M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures] Vaclav Kotesovec, Plot of Sum_{k=1..n} a(k) / (108*n^2/Pi^6) for n = 1..1000000 N. J. A. Sloane, Transforms FORMULA Multiplicative with a(p^e) = Sum_{k=0..3} (-1)^k C(3,k)*p^(e-k)[e>=k]; Dirichlet g.f.: zeta(s-1)/zeta^3(s). a(n) = Sum{d|n} tau_{-3}(d)*n/d = Sum{d|n} tau_{-2}(d)*phi(n/d), where tau_{-3} is A007428 and tau_{-2} is A007427. - Enrique Pérez Herrero, Jan 19 2013 Sum_{k=1..n} a(k) ~ 108 * n^2 / Pi^6. - Vaclav Kotesovec, Nov 04 2018 MATHEMATICA a[p_, e_] := Sum[ (-1)^k*Binomial[3, k]*p^(e - k), {k, 0, Min[e, 3]}]; a[n_] := Times @@ Apply[a, FactorInteger[n], {1}]; a[1] = 1; Table[ a[n], {n, 1, 68}] (* Jean-François Alcover, Dec 28 2011, after formula *) CROSSREFS Cf. A007431. Sequence in context: A347961 A020781 A327883 * A079124 A242071 A176910 Adjacent sequences: A007429 A007430 A007431 * A007433 A007434 A007435 KEYWORD sign,easy,nice,mult AUTHOR STATUS approved

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Last modified November 26 21:15 EST 2022. Contains 358362 sequences. (Running on oeis4.)