A130156 a(0)=1. a(n) = number of earlier terms of the sequence that divide the n-th Fibonacci number.

1, 1, 2, 3, 3, 2, 4, 2, 4, 5, 3, 2, 11, 2, 2, 9, 5, 2, 11, 2, 9, 10, 2, 2, 19, 4, 2, 13, 6, 2, 22, 2, 5, 15, 2, 6, 27, 2, 2, 18, 11, 2, 23, 2, 5, 25, 2, 2, 34, 3, 10, 22, 6, 2, 28, 6, 7, 23, 2, 2, 51, 2, 2, 29, 7, 6, 30, 2, 6, 28, 11, 2, 55, 2, 2, 38, 6, 3, 34, 2, 19, 34, 2, 2, 54, 6, 2, 35, 9, 2

Offset

0,3

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Example

The 10th Fibonacci number is 55. Among terms (a(0), a(1),..., a(9)) there are 3 terms (a(0)=1, a(1)=1, a(9)=5)) that divide 55, so a(10) = 3.

Maple

A130156 := proc(nmax) local a, nfib, anew, i, n; a := [1] ; while nops(a) < nmax do n := nops(a) ; 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: A130156(100) ; # R. J. Mathar, Jun 07 2007

Prog

(PARI)
up_to = 16384;
A130156list(upto_n) = { my(v=vector(1+upto_n), fibo); v[1] = 1; for(n=2, #v, fibo = fibonacci(n-1); v[n] = sum(i=1, n-1, !(fibo%v[i]))); (v); };
v130156 = A130156list(up_to);
A130156(n) = v130156[1+n]; \\ Antti Karttunen, Feb 18 2023

Crossrefs

Cf. A130155.

Sequence in context: A235343 A236456 A046824 * A139169 A238444 A076742

Adjacent sequences: A130153 A130154 A130155 * A130157 A130158 A130159

Keyword

nonn,look

Author

Leroy Quet, May 13 2007

Extensions

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

Status

approved