

A220137


Numerator of the fraction of Fibonacci numbers divisible by n.


2



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
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OFFSET

2,1


LINKS

T. D. Noe, Table of n, a(n) for n = 2..10000
Paul S. Bruckman and Peter G. Anderson, Conjectures on the Zdensities of the Fibonacci sequence, Fibonacci Quart. 36 (1998), no. 3, 263271.
Paul Cubre and Jeremy Rouse, Divisibility properties of the Fibonacci entry point, arxiv 1212.6221
T. D. Noe, Plot of the logarithm of the fraction


EXAMPLE

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.


MATHEMATICA

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}]]


CROSSREFS

Cf. A000045 (Fibonacci numbers), A220138 (denominator).
Sequence in context: A249386 A089026 A080305 * A053815 A194446 A251758
Adjacent sequences: A220134 A220135 A220136 * A220138 A220139 A220140


KEYWORD

nonn,frac


AUTHOR

T. D. Noe, Dec 30 2012


STATUS

approved



