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A086599 Number of prime factors in Lucas(n), counting multiplicity.

%I A086599 #20 Jun 15 2025 10:58:39
%S A086599 1,0,1,2,1,1,3,1,1,3,2,1,3,1,2,4,1,1,5,1,2,4,3,2,3,3,2,4,3,2,5,1,2,4,
%T A086599 3,4,4,1,2,5,3,1,6,2,4,7,3,1,4,2,4,5,3,1,7,5,2,5,3,3,6,1,2,7,2,5,6,2,
%U A086599 2,6,4,1,4,2,3,8,2,4,5,1,2,6,4,2,7,4,2,6,3,2,8,3,3,5,4,5,4,2,4,8,4,3,7,3,4,10
%N A086599 Number of prime factors in Lucas(n), counting multiplicity.
%H A086599 Max Alekseyev, <a href="/A086599/b086599.txt">Table of n, a(n) for n = 0..1411</a> (first 1000 terms from Amiram Eldar)
%H A086599 Blair Kelly, <a href="http://mersennus.net/fibonacci//">Fibonacci and Lucas Factorizations</a>
%H A086599 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LucasNumber.html">Lucas Number</a>
%t A086599 Lucas[n_] := Fibonacci[n+1] + Fibonacci[n-1]; Join[{0}, Table[Plus@@(Transpose[FactorInteger[Lucas[n]]][[2]]), {n, 2, 150}]]
%o A086599 (PARI) a(n)=bigomega(fibonacci(n-1)+fibonacci(n+1)) \\ _Charles R Greathouse IV_, Sep 14 2015
%Y A086599 Cf. A000204 (Lucas numbers), A086598 (number of distinct prime factors), A086600 (number of primitive prime factors).
%K A086599 hard,nonn
%O A086599 0,4
%A A086599 _T. D. Noe_, Jul 24 2003
%E A086599 a(0) added by _Amiram Eldar_, Sep 01 2019