A220138 Denominator of the fraction of Fibonacci numbers divisible by n.

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

T. D. Noe, Table of n, a(n) for n = 2..10000

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: A233129 A035292 A144457 * A146975 A046970 A322360

Adjacent sequences: A220135 A220136 A220137 * A220139 A220140 A220141

Keyword

nonn,frac

Author

T. D. Noe, Dec 30 2012

Status

approved