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A007432
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Moebius transform applied thrice to natural numbers.
(Formerly M0031)
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1
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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; internal format)
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OFFSET
| 1,5
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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.
N. J. A. Sloane, Transforms
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FORMULA
| Multiplicative with a(p^e) = sum (-1)^k (3 choose k)p^(e-k)[e>=k], k=0..3
Dirichlet g.f.: zeta(x-1)/zeta^3(x)
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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}] (* From Jean-François Alcover, Dec 28 2011, after formula *)
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CROSSREFS
| Sequence in context: A154794 A177264 A020781 * A079124 A176910 A056737
Adjacent sequences: A007429 A007430 A007431 * A007433 A007434 A007435
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KEYWORD
| sign,easy,nice,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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