Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Jan 12 2017 07:17:53
%S 1,1,1,1,1,2,1,3,2,5,1,8,1,13,5,21,1,34,1,55,13,89,1,144,5,233,34,377,
%T 1,610,1,987,89,1597,13,2584,1,4181,233,6765,1,10946,1,17711,610,
%U 28657,1,46368,13,75025,1597,121393,1,196418,89,317811,4181,514229,1,832040,1
%N Greatest Fibonacci number that is a proper divisor of the n-th Fibonacci number; a(1) = a(2) = 1.
%C a(A001605(n)) = 1.
%H Antti Karttunen, <a href="/A105800/b105800.txt">Table of n, a(n) for n = 1..987</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Divisibility_sequence">Divisibility sequence</a>
%F From _Antti Karttunen_, Jan 11 2017: (Start)
%F a(n) = A280686(A000045(n)).
%F a(n) = A000045(A032742(n)). [Because A000045 is a divisibility sequence.]
%F a(A032742(n)) = A280688(n).
%F (End)
%t nn=70;Join[{1,1},With[{fibs=Fibonacci[Range[nn]]},Table[ Max[ Intersection[ Most[Divisors[fibs[[n]]]],fibs]],{n,3,nn}]]] (* _Harvey P. Dale_, Apr 10 2012 *)
%Y Cf. A000045, A032742, A076984, A139045, A280686, A280688, A280689, A280690, A280698, A280699.
%Y Cf. A046022 (gives the positions of ones).
%K nonn
%O 1,6
%A _Reinhard Zumkeller_, Apr 20 2005