A006876 Mu-molecules in Mandelbrot set whose seeds have period n.

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

Author

Robert Munafo

Keywords

• nonn

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

Crossrefs

Cf. A006874, A006875, A000740, A118454.

Programs

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}] (* Cheng Zhang, Apr 02 2012 *)

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

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

Extensions

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

More terms from Cheng Zhang, Apr 02 2012