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Search: id:A006874
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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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+0
3
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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; listen)
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OFFSET
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1,3
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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.
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LINKS
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R. P. Munafo, Mu-Ency - The Encyclopedia of the Mandelbrot Set
F. V. Weinstein, Notes on Fibonacci partitions
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FORMULA
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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.yu), Feb 09 2002
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EXAMPLE
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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
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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
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Cf. A006875, A006876.
Sequence in context: A094871 A079667 A073061 this_sequence A034890 A009490 A064778
Adjacent sequences: A006871 A006872 A006873 this_sequence A006875 A006876 A006877
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KEYWORD
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nonn
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AUTHOR
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mrob(AT)mrob.com (Robert P Munafo)
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 09 2002
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