A220137 - OEIS

A220137

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

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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 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

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