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A006874
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Mu-atoms of period n on continent of Mandelbrot set.
(Formerly M0535)
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2
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1, 1, 2, 3, 4, 6, 6, 9, 10, 12, 10, 22, 12, 18, 24, 27, 16, 38, 18, 44, 36, 30, 22, 78, 36, 36, 50, 66, 28, 104, 30, 81, 60, 48, 72, 158, 36, 54, 72, 156, 40, 156, 42, 110, 152, 66, 46, 270, 78, 140, 96, 132, 52, 230, 120, 234, 108, 84, 58, 456, 60, 90, 228, 243, 144, 260
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| 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
| R. P. Munafo, Mu-Ency - The Encyclopedia of the Mandelbrot Set
F. V. Weinstein, Notes on Fibonacci partitions
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FORMULA
| a(n) = Sum_{ d divides n, d<n} phi(n/d)*a(d), n>1, a(1)=1, where phi is Euler totient function (A000010). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 09 2002
a(n) = if n=1 then 1 else SUM(a(GCD(n,k)): 1<=k<n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 25 2009]
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EXAMPLE
| a(1)=1, a(2)=a(1), a(3)=2*a(1), a(4)=2*a(1)+a(2), a(5)=4*a(1), a(6)=2*a(1)+2*a(2)+a(3), a(7)=6*a(1), a(8)=4*a(1)+2*a(2)+a(4), a(9)=6*a(1)+2*a(3), a(10)=4*a(1)+4*a(2)+a(5), a(11)=10*a(1), a(12)=4*a(1)+2*a(2)+2*a(3)+2*a(4)+a(6),...
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MATHEMATICA
| a[1] = 1; a[n_] := a[n] = Block[{d = Most@Divisors@n}, Plus @@ (EulerPhi[n/d]*a /@ d)]; Array[a, 66] (from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 22 2005)
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CROSSREFS
| Cf. A006875, A006876.
Sequence in context: A195013 A079667 A073061 * A034890 A009490 A064778
Adjacent sequences: A006871 A006872 A006873 * A006875 A006876 A006877
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KEYWORD
| nonn
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AUTHOR
| mrob(AT)mrob.com (Robert P Munafo)
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 09 2002
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