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Mu-molecules in Mandelbrot set whose seeds have period n.
(Formerly M2883)
4

%I M2883 #24 Feb 25 2013 17:23:13

%S 1,0,1,3,11,20,57,108,240,472,1013,1959,4083,8052,16315,32496,65519,

%T 130464,262125,523209,1048353,2095084,4194281,8384100,16777120,

%U 33546216,67108068,134201223,268435427,536836484,1073741793,2147417952,4294964173,8589803488,17179868739

%N Mu-molecules in Mandelbrot set whose seeds have period n.

%D B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, NY, 1982, p. 183.

%D R. Penrose, The Emperor's New Mind, Penguin Books, NY, 1991, p. 138.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Cheng Zhang, <a href="/A006876/b006876.txt">Table of n, a(n) for n = 1..1000</a>

%H R. P. Munafo, <a href="http://www.mrob.com/pub/muency/enumerationoffeatures.html">Enumeration of Features</a>

%F 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

%t 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 *)

%o (PARI) A000740(n)=sumdiv(n,d,moebius(n/d)<<(d-1))

%o a(n)=2*A000740(n)-sumdiv(n, d, eulerphi(n/d)*A000740(d)) \\ _Charles R Greathouse IV_, Feb 18 2013

%Y Cf. A006874, A006875, A000740, A118454.

%K nonn

%O 1,4

%A _Robert Munafo_

%E Web link changed to more relevant page by _Robert Munafo_, Nov 16 2010

%E More terms from _Cheng Zhang_, Apr 02 2012