

A115051


Number of distinct prime factors of F(n + L(n)) where F(n) is the Fibonacci number and L(n) is the Lucas number and n >= 2.


1



1, 1, 1, 3, 4, 5, 4, 4, 6, 15, 4, 9, 3, 8, 22, 42, 61
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OFFSET

2,4


COMMENTS

Added a(13)=9 from F(534) and a(14)=3 from F(857) using Kelly's factorizations. a(15)>=5 via F(1379) and a(16)=22 via F(2223).  R. J. Mathar, Apr 23 2006


LINKS



EXAMPLE

The first three terms are 1 since:
F(2 + L(2)) = 5 (a prime)
F(3 + L(3)) = 13 (a prime)
F(4 + L(4)) = 89 (a prime)


MAPLE

lucas := proc(n::integer) if n = 0 then RETURN(2) ; elif n = 1 then RETURN(1) ; else RETURN(combinat[fibonacci](n1)+combinat[fibonacci](n+1)) ; fi ; end : for n from 2 to 100 do print(n+lucas(n), "...") ; tst := combinat[fibonacci](n+lucas(n)) ; an := nops(op(2, ifactors(tst))) ; print(an) ; od : # R. J. Mathar, Apr 23 2006


MATHEMATICA

Table[PrimeNu[Fibonacci[n+LucasL[n]]], {n, 2, 15}] (* Harvey P. Dale, Nov 12 2016 *)


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS

Offset corrected and a(15)a(18) added from factordb.com by Amiram Eldar, Feb 12 2020


STATUS

approved



