A006876 Mu-molecules in Mandelbrot set whose seeds have period n. (Formerly M2883)

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

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: A139221 A300381 A363012 * A031239 A088619 A031318

Adjacent sequences: A006873 A006874 A006875 * A006877 A006878 A006879

Keyword

nonn

Author

Robert Munafo

Extensions

Web link changed to more relevant page by Robert Munafo, Nov 16 2010

More terms from Cheng Zhang, Apr 02 2012

Status

approved