A120481 - OEIS

%I #10 May 25 2020 17:14:23

%S 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,

%T 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,

%U 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

%N 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.

%C Prime divisors counted without multiplicity. - _Harvey P. Dale_, May 25 2020

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LucasNumber.html">Lucas Number</a>

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

%t Do[f = Fibonacci[n]; l = Fibonacci[n-1] + Fibonacci[n+1]; Print[Length[FactorInteger[f + l]]], {n, 100}]

%t Table[PrimeNu[Fibonacci[n]+LucasL[n]],{n,100}] (* _Harvey P. Dale_, May 25 2020 *)

%K nonn

%O 1,3

%A _Ryan Propper_, Jul 21 2006

%E Definition clarified by _Harvey P. Dale_, May 25 2020