%I #11 Apr 23 2013 19:27:28

%S 2,3,1,5,1,7,1,1,25,11,1,13,7,5,1,17,1,19,5,7,11,23,1,1,13,1,7,29,25,

%T 31,1,11,17,35,1,37,19,13,5,41,7,43,11,5,23,47,1,1,5,17,13,53,1,11,7,

%U 19,29,59,5,61,31,7,1,65,11,67,17,23,175,71,1,73,37

%N Numerator of the fraction of Fibonacci numbers divisible by n.

%H T. D. Noe, <a href="/A220137/b220137.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

%H T. D. Noe, <a href="/A220137/a220137.gif">Plot of the logarithm of the fraction</a>

%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]]; Numerator[Table[rho[n] * Times @@ Table[psi[i], {i, FactorInteger[n]}], {n, 2, 100}]]

%Y Cf. A000045 (Fibonacci numbers), A220138 (denominator).

%K nonn,frac

%O 2,1

%A _T. D. Noe_, Dec 30 2012