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A006876
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Mu-molecules in Mandelbrot set whose seeds have period n.
(Formerly M2883)
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4
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1, 0, 1, 3, 11, 20, 57, 108, 240, 472, 1013, 1959, 4083, 8052, 16315, 32496, 65519, 130464, 262125, 523209, 1048353, 2095084, 4194281, 8384100, 16777120, 33546216, 67108068, 134201223, 268435427, 536836484, 1073741793, 2147417952, 4294964173, 8589803488, 17179868739
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,4
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REFERENCES
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B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, NY, 1982, p. 183.
R. Penrose, The Emperor's New Mind, Penguin Books, NY, 1991, p. 138.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Cheng Zhang, Table of n, a(n) for n = 1..1000
R. P. Munafo, Enumeration of Features
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FORMULA
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a(n) = 2*l(n) - sum_{d|n} phi(n/d)*l(d), where l(n) = sum_{d|n} mu(n/d) 2^(d-1) (A000740), and phi(n) and mu(n) are the Euler totient function (A000010) and Moebius function (A008683), respectively. - Cheng Zhang, Apr 02 2012
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MATHEMATICA
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degRp[n_] := Sum[MoebiusMu[n/d] 2^(d - 1), {d, Divisors[n]}]; Table[degRp[n]*2 - Sum[EulerPhi[n/d] degRp[d], {d, Divisors[n]}], {n, 1, 100}] (* from Cheng Zhang, Apr 02 2012 *)
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PROG
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(PARI) A000740(n)=sumdiv(n, d, moebius(n/d)<<(d-1))
a(n)=2*A000740(n)-sumdiv(n, d, eulerphi(n/d)*A000740(d)) \\ Charles R Greathouse IV, Feb 18 2013
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CROSSREFS
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Cf. A006874, A006875, A000740, A118454.
Sequence in context: A139220 A139221 A300381 * A031239 A088619 A031318
Adjacent sequences: A006873 A006874 A006875 * A006877 A006878 A006879
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KEYWORD
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nonn
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AUTHOR
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Robert Munafo
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EXTENSIONS
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Web link changed to more relevant page by Robert Munafo, Nov 16 2010
More terms from Cheng Zhang, Apr 02 2012
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STATUS
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approved
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