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 A006876 Mu-molecules in Mandelbrot set whose seeds have period n. (Formerly M2883) 4
 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)
 OFFSET 1,4 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). LINKS Cheng Zhang, Table of n, a(n) for n = 1..1000 R. P. Munafo, Enumeration of Features FORMULA 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 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A006874, A006875, A000740, A118454. Sequence in context: A139220 A139221 A300381 * A031239 A088619 A031318 Adjacent sequences: A006873 A006874 A006875 * A006877 A006878 A006879 KEYWORD nonn AUTHOR EXTENSIONS Web link changed to more relevant page by Robert Munafo, Nov 16 2010 More terms from Cheng Zhang, Apr 02 2012 STATUS approved

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Last modified January 29 17:53 EST 2023. Contains 359925 sequences. (Running on oeis4.)