A083019 Number of common divisors of n and F(n) where F(n) denotes the n-th Fibonacci number.

1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 6, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 8, 3, 1, 1, 1, 1, 4, 1, 1, 1, 1, 2, 9, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 10, 1, 3, 1, 1, 1, 2, 2, 2, 1, 1, 1, 12, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 12, 1, 1, 3, 1, 1, 2, 1, 2, 1, 1, 1, 6, 2, 1, 1, 1, 1, 4, 2, 1, 1, 1, 2, 12, 1, 1, 1, 3, 1, 2, 1

Offset: 1

Author

Benoit Cloitre, May 31 2003

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000045, A104714.

Programs

Mathematica

Table[Length[Intersection[Divisors[n],Divisors[Fibonacci[n]]]],{n,120}] (* Harvey P. Dale, Aug 24 2014 *)
a[n_] := DivisorSigma[0, GCD[n, Fibonacci[n]]]; Array[a, 100] (* Amiram Eldar, Oct 18 2019 *)

PARI

a(n) = length(setintersect(divisors(n), divisors(fibonacci(n)))); \\ Michel Marcus, Dec 04 2013

Formula

a(n) = A000005(A104714(n)). - Amiram Eldar, Jun 09 2022