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

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, 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, 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

Offset: 0

Author

T. D. Noe, Jul 24 2003

Keywords

• hard
• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 0..1411 (first 1000 terms from Amiram Eldar)
• Blair Kelly, Fibonacci and Lucas Factorizations
• Eric Weisstein's World of Mathematics, Lucas Number

Crossrefs

Cf. A000204 (Lucas numbers), A086598 (number of distinct prime factors), A086600 (number of primitive prime factors).

Programs

Mathematica

Lucas[n_] := Fibonacci[n+1] + Fibonacci[n-1]; Join[{0}, Table[Plus@@(Transpose[FactorInteger[Lucas[n]]][[2]]), {n, 2, 150}]]

PARI

a(n)=bigomega(fibonacci(n-1)+fibonacci(n+1)) \\ Charles R Greathouse IV, Sep 14 2015

Extensions

a(0) added by Amiram Eldar, Sep 01 2019