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

0,4

Links

Amiram Eldar, Table of n, a(n) for n = 0..1000 (using Blair Kelly's data)

Blair Kelly, Fibonacci and Lucas Factorizations

Eric Weisstein's World of Mathematics, Lucas Number

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A300650 A363528 A300649 * A371209 A353947 A181846

Adjacent sequences: A086596 A086597 A086598 * A086600 A086601 A086602

Keyword

hard,nonn

Author

T. D. Noe, Jul 24 2003

Extensions

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

Status

approved