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A005086 Number of Fibonacci numbers 1,2,3,5,... dividing n. 19
1, 2, 2, 2, 2, 3, 1, 3, 2, 3, 1, 3, 2, 2, 3, 3, 1, 3, 1, 3, 3, 2, 1, 4, 2, 3, 2, 2, 1, 4, 1, 3, 2, 3, 2, 3, 1, 2, 3, 4, 1, 4, 1, 2, 3, 2, 1, 4, 1, 3, 2, 3, 1, 3, 3, 3, 2, 2, 1, 4, 1, 2, 3, 3, 3, 3, 1, 3, 2, 3, 1, 4, 1, 2, 3, 2, 1, 4, 1, 4, 2, 2, 1, 4, 2, 2, 2, 3, 2, 4, 2, 2, 2, 2, 2, 4, 1, 2, 2, 3, 1, 4, 1, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) <= A072649(n). - Robert G. Wilson v, Dec 10 2006

Indices of records are in A129655. - R. J. Mathar, Nov 02 2007

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

Equals A051731 * A010056. - Gary W. Adamson, Nov 06 2007

G.f.: sum_{n>=2} x^F(n)/(1-x^F(n)) where F(n)=A000045(n). - Joerg Arndt, Jan 06 2015

MAPLE

with(combinat): for n from 1 to 200 do printf(`%d, `, sum(floor(n/fibonacci(k))-floor((n-1)/fibonacci(k)), k=2..15)) od:

MATHEMATICA

f[n_] := Block[{k = 1}, While[Fibonacci[k] <= n, k++ ]; Count[ Mod[n, Array[ Fibonacci, k - 1]], 0] - 1]; Array[f, 105] (* Robert G. Wilson v, Dec 10 2006 *)

PROG

(PARI) isfib(n)=my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8))

a(n)=sumdiv(n, d, isfib(d)) \\ Charles R Greathouse IV, Nov 06 2014

CROSSREFS

Cf. A038663, A051731, A010056.

Sequence in context: A063473 A096859 A301304 * A237168 A157372 A270559

Adjacent sequences:  A005083 A005084 A005085 * A005087 A005088 A005089

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers, Feb 19 2001

Incorrect comment removed by Charles R Greathouse IV, Nov 06 2014

STATUS

approved

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Last modified October 17 21:37 EDT 2019. Contains 328134 sequences. (Running on oeis4.)