|
%I #10 Apr 23 2013 19:26:47
%S 3,8,3,24,4,48,6,8,144,120,8,168,72,64,12,288,12,360,144,128,180,528,
%T 16,24,252,24,144,840,384,960,24,320,432,1152,24,1368,540,448,288,
%U 1680,192,1848,360,192,792,2208,32,48,144,768,504,2808,36,576,288,960
%N Denominator of the fraction of Fibonacci numbers divisible by n.
%H T. D. Noe, <a href="/A220138/b220138.txt">Table of n, a(n) for n = 2..10000</a>
%H Paul S. Bruckman and Peter G. Anderson, <a href="http://www.fq.math.ca/36-3.html">Conjectures on the Z-densities of the Fibonacci sequence</a>, Fibonacci Quart. 36 (1998), no. 3, 263-271.
%H Paul Cubre and Jeremy Rouse, <a href="http://arxiv.org/abs/1212.6221">Divisibility properties of the Fibonacci entry point</a>, arxiv 1212.6221
%e For n = 2 to 10, the fractions are 2/3, 3/8, 1/3, 5/24, 1/4, 7/48, 1/6, 1/8, 25/144.
%t psi[{q_, e_}] := q^(2 - e)/(q^2 - 1); rho[m_] := If[Mod[m, 20] == 0, 1/2, If[Mod[m, 20] == 10, 5/4, 1]]; Denominator[Table[rho[n] * Times @@ Table[psi[i], {i, FactorInteger[n]}], {n, 2, 100}]]
%Y Cf. A000045 (Fibonacci numbers), A220137 (numerator).
%K nonn,frac
%O 2,1
%A _T. D. Noe_, Dec 30 2012
|
