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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 11:28 EST 2022. Contains 350477 sequences. (Running on oeis4.)