A120481 Number of distinct prime divisors of F(n) + L(n), where F(n) is the n-th Fibonacci number and L(n) is the n-th Lucas number.

1, 1, 2, 2, 1, 2, 3, 2, 3, 2, 2, 2, 3, 3, 4, 2, 3, 3, 5, 3, 3, 2, 4, 3, 3, 4, 5, 2, 5, 3, 5, 3, 3, 4, 5, 4, 4, 3, 7, 3, 5, 2, 6, 5, 4, 2, 6, 4, 6, 3, 5, 3, 6, 5, 7, 5, 4, 3, 8, 3, 4, 5, 7, 4, 5, 4, 6, 5, 8, 3, 8, 3, 5, 5, 6, 5, 6, 3, 10, 7, 4, 2, 9, 5, 4, 4, 10, 3, 10, 5, 7, 4, 3, 7, 9, 5, 6, 6, 10, 3

Offset

1,3

Comments

Prime divisors counted without multiplicity. - Harvey P. Dale, May 25 2020

Links

Table of n, a(n) for n=1..100.

Eric Weisstein's World of Mathematics, Fibonacci Number

Eric Weisstein's World of Mathematics, Lucas Number

Example

F(30) + L(30) = 2692538, which has the 3 prime divisors {2, 557, 2417}, so a(30) = 3.

Mathematica

Do[f = Fibonacci[n]; l = Fibonacci[n-1] + Fibonacci[n+1]; Print[Length[FactorInteger[f + l]]], {n, 100}]
Table[PrimeNu[Fibonacci[n]+LucasL[n]], {n, 100}] (* Harvey P. Dale, May 25 2020 *)

Crossrefs

Sequence in context: A365836 A331244 A316845 * A369067 A356647 A219644

Adjacent sequences: A120478 A120479 A120480 * A120482 A120483 A120484

Keyword

nonn

Author

Ryan Propper, Jul 21 2006

Extensions

Definition clarified by Harvey P. Dale, May 25 2020

Status

approved