A139045 Largest proper divisor of the Fibonacci numbers > 1.

1, 1, 1, 4, 1, 7, 17, 11, 1, 72, 1, 29, 305, 329, 1, 1292, 113, 2255, 5473, 199, 1, 23184, 15005, 521, 98209, 105937, 1, 416020, 2417, 726103, 1762289, 3571, 1845493, 7465176, 330929, 1056437, 31622993, 34111385, 59369, 133957148, 1, 233802911, 567451585

Offset: 3

Author

Omar E. Pol, Apr 23 2008

Keywords

• nonn

Comments

See the list of divisors of positive Fibonacci numbers in the triangle A133021.

See the largest proper divisor of n in A032742.

Fibonacci(1)=Fibonacci(2)=1 do not have proper divisors. - Emeric Deutsch, May 18 2008

Examples

			a(9) = 17 because the 9th Fibonacci number is 34 and the divisors of 34 are 1, 2, 17, 34, then the largest proper divisor of 34 is 17.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 3..1000

Crossrefs

Cf. A000045, A032742, A060383, A133021, A133028, A134708.

Programs

Maple

with(combinat): with(numtheory): a:=proc(n) options operator, arrow: op(tau(fibonacci(n))-1, divisors(fibonacci(n))) end proc: seq(a(n),n=3..40); # Emeric Deutsch, May 18 2008
# second Maple program:
a:= n-> (f-> f/min(numtheory[factorset](f)))((<<0|1>, <1|1>>^n)[1, 2]):
seq(a(n), n=3..47);  # Alois P. Heinz, Sep 03 2019

Mathematica

lpd[n_]:=Divisors[n][[-2]]; lpd/@(Fibonacci[Range[3,40]]) (* Harvey P. Dale, Mar 29 2015 *)

Formula

a(n) = A032742(A000045(n)).

a(n) = A000045(n)/A060383(n). - Alois P. Heinz, Sep 03 2019

Extensions

More terms from Emeric Deutsch, May 18 2008