OFFSET
1,3
COMMENTS
Definitions and Maxima source code on second Munafo web page. - Robert Munafo, Dec 12 2009
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
Indranil Ghosh, Table of n, a(n) for n = 1..1000
R. P. Munafo, Mu-Ency - The Encyclopedia of the Mandelbrot Set
R. Munafo, Enumeration of Features [From Robert Munafo, Dec 12 2009]
FORMULA
a(n) = Sum_{d|n, d < n} (phi(n/d) * sum_{c|d} (mu(d/c) 2^(c-1))), where phi(n) and mu(n) are the Euler totient function (A000010) and Moebius function (A008683), respectively. - Cheng Zhang, Apr 03 2012
EXAMPLE
From Robert Munafo, Dec 12 2009: (Start)
For n=1 the only mu-atom is the large cardioid, which is a seed.
For n=2 there is one, the large circular mu-atom centered at -1+0i, so a(2)=1.
For n=3 there is a seed (cardioid) at -1.75+0i, which doesn't count, and two non-seeds ("circles") at approx. -0.1225+-0.7448i, so a(3)=2. (End)
MATHEMATICA
Table[Sum[EulerPhi[n/d] Sum[MoebiusMu[d/c] 2^(c - 1), {c, Divisors[d]}], {d, Drop[Divisors[n], -1]}], {n, 1, 100}] (* Cheng Zhang, Apr 03 2012 *)
PROG
(Python)
from sympy import divisors, totient, mobius
l=[0, 0]
for n in range(2, 101):
l.append(sum(totient(n//d)*sum(mobius(d//c)*2**(c - 1) for c in divisors(d)) for d in divisors(n)[:-1]))
print(l[1:]) # Indranil Ghosh, Jul 12 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved