A105800 Greatest Fibonacci number that is a proper divisor of the n-th Fibonacci number; a(1) = a(2) = 1.

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, 1, 610, 1, 987, 89, 1597, 13, 2584, 1, 4181, 233, 6765, 1, 10946, 1, 17711, 610, 28657, 1, 46368, 13, 75025, 1597, 121393, 1, 196418, 89, 317811, 4181, 514229, 1, 832040, 1

Offset: 1

Author

Reinhard Zumkeller, Apr 20 2005

Keywords

• nonn

Comments

a(A001605(n)) = 1.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..987
• Eric Weisstein's World of Mathematics, Fibonacci Number
• Wikipedia, Divisibility sequence

Crossrefs

Cf. A000045, A032742, A076984, A139045, A280686, A280688, A280689, A280690, A280698, A280699.

Cf. A046022 (gives the positions of ones).

Programs

Mathematica

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 *)

Formula

From Antti Karttunen, Jan 11 2017: (Start)

a(n) = A280686(A000045(n)).

a(n) = A000045(A032742(n)). [Because A000045 is a divisibility sequence.]

a(A032742(n)) = A280688(n).

(End)