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Paul S. Bruckman and Peter G. Anderson, Conjectures on the Z-densities of the Fibonacci sequence, Fibonacci Quart. 36 (1998), no. 3, 263-271.
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.
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proposed
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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.
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Paul Cubre and Jeremy Rouse, <a href="http://arxiv.org/abs/1212.6221">Divisibility properties of the Fibonacci entry point</a>, arxiv 1212.6221
Paul Cubre and Jeremy Rouse, <a href="http://arxiv.org/abs/1212.6221">Divisibility properties of the Fibonacci entry point</a>, arxiv 1212.6221
T. D. Noe, <a href="/A220137/a220137.gif">Plot of the logarithm of the fraction</a>
T. D. Noe, <a href="/A220137/b220137.txt">Table of n, a(n) for n = 2..10000</a>
allocated for T. D. Noe
Numerator of the fraction of Fibonacci numbers divisible by n.
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, 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, 19, 29, 59, 5, 61, 31, 7, 1, 65, 11, 67, 17, 23, 175, 71, 1, 73, 37
2,1
Paul S. Bruckman and Peter G. Anderson, Conjectures on the Z-densities of the Fibonacci sequence, Fibonacci Quart. 36 (1998), no. 3, 263-271.
Paul Cubre and Jeremy Rouse, <a href="http://arxiv.org/abs/1212.6221">Divisibility properties of the Fibonacci entry point</a>, arxiv 1212.6221
For 2 to 10, the fractions are 2/3, 3/8, 1/3, 5/24, 1/4, 7/48, 1/6, 1/8, 25/144.
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}]]
Cf. A220138 (denominator).
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nonn,frac
T. D. Noe, Dec 30 2012
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