A130155 a(1)=1. a(n) = number of earlier terms of the sequence that divide the n-th Fibonacci number.

1, 1, 2, 2, 2, 5, 2, 2, 7, 3, 2, 9, 2, 2, 11, 4, 2, 12, 2, 5, 12, 2, 2, 20, 4, 2, 15, 3, 2, 22, 2, 5, 17, 2, 5, 26, 2, 2, 20, 11, 2, 24, 2, 4, 27, 2, 2, 34, 2, 8, 25, 4, 2, 33, 6, 5, 26, 2, 2, 52, 2, 2, 34, 5, 8, 36, 2, 4, 31, 10, 2, 52, 2, 2, 42, 4, 2, 43, 2, 15, 39, 2, 2, 59, 8, 2, 39, 6, 2, 65, 2

Offset

1,3

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Example

The 10th Fibonacci number is 55. Among terms (a(1), a(2), ..., a(9)) there are 3 terms (a(1)=1, a(2)=1, a(6)=5)) that divide 55, so a(10) = 3.

Maple

A130155 := proc(nmax) local a, nfib, anew, i; a := [1] ; while nops(a) < nmax do n := nops(a)+1 ; nfib := combinat[fibonacci](n) ; anew :=0 ; for i from 1 to nops(a) do if nfib mod op(i, a) = 0 then anew := anew+1 ; fi ; od ; a := [op(a), anew] ; od ; RETURN(a) ; end: A130155(100) ; # R. J. Mathar, Jun 07 2007

Mathematica

seq[nmax_] := Module[{a, nfib, anew, i}, a = {1}; While[Length[a] < nmax , n = Length[a]+1; nfib = Fibonacci[n]; anew = 0; For[i = 1, i <= Length[a], i++, If[Mod[ nfib, a[[i]]] == 0 , anew = anew+1]]; AppendTo[a, anew]]; Return[a]]; seq[100] (* Jean-François Alcover, Nov 18 2013, translated from Maple *)
nn = 1000; t = {1}; Do[cnt = 0; fibn = Fibonacci[n]; Do[If[Mod[fibn, t[[k]]] == 0, cnt++], {k, n - 1}]; AppendTo[t, cnt], {n, 2, nn}]; t (* T. D. Noe, Nov 18 2013 *)

Crossrefs

Cf. A130156.

Sequence in context: A112659 A342550 A115281 * A350403 A113516 A226525

Adjacent sequences: A130152 A130153 A130154 * A130156 A130157 A130158

Keyword

nonn

Author

Leroy Quet, May 13 2007

Extensions

More terms from R. J. Mathar, Jun 07 2007

Status

approved