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A220138
Denominator of the fraction of Fibonacci numbers divisible by n.
2
3, 8, 3, 24, 4, 48, 6, 8, 144, 120, 8, 168, 72, 64, 12, 288, 12, 360, 144, 128, 180, 528, 16, 24, 252, 24, 144, 840, 384, 960, 24, 320, 432, 1152, 24, 1368, 540, 448, 288, 1680, 192, 1848, 360, 192, 792, 2208, 32, 48, 144, 768, 504, 2808, 36, 576, 288, 960
OFFSET
2,1
LINKS
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, Divisibility properties of the Fibonacci entry point, arxiv 1212.6221
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]]; Denominator[Table[rho[n] * Times @@ Table[psi[i], {i, FactorInteger[n]}], {n, 2, 100}]]
CROSSREFS
Cf. A000045 (Fibonacci numbers), A220137 (numerator).
Sequence in context: A035292 A387661 A144457 * A146975 A046970 A322360
KEYWORD
nonn,frac
AUTHOR
T. D. Noe, Dec 30 2012
STATUS
approved