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%I #15 Aug 24 2015 02:19:55
%S 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,
%T 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,
%U 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
%N a(1)=1. a(n) = number of earlier terms of the sequence that divide the n-th Fibonacci number.
%H T. D. Noe, <a href="/A130155/b130155.txt">Table of n, a(n) for n = 1..1000</a>
%e 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.
%p 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
%t 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 *)
%t 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 *)
%Y Cf. A130156.
%K nonn
%O 1,3
%A _Leroy Quet_, May 13 2007
%E More terms from _R. J. Mathar_, Jun 07 2007
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