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 A086598 Number of distinct prime factors in Lucas(n). 6
 0, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 3, 1, 2, 3, 1, 1, 3, 1, 2, 3, 3, 2, 3, 3, 2, 3, 2, 2, 4, 1, 2, 3, 3, 4, 4, 1, 2, 4, 3, 1, 5, 2, 4, 6, 3, 1, 4, 2, 4, 4, 3, 1, 4, 4, 2, 4, 3, 3, 6, 1, 2, 6, 2, 5, 5, 2, 2, 5, 4, 1, 4, 2, 3, 7, 2, 4, 4, 1, 2, 5, 4, 2, 6, 4, 2, 5, 3, 2, 6, 3, 3, 4, 4, 5, 4, 2, 4, 7, 4, 3, 6, 3, 4, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Interestingly, the Lucas numbers separate the primes into three disjoint sets: (A053028) primes that do not divide any Lucas number, (A053027) primes that divide Lucas numbers of even index and (A053032) primes that divide Lucas numbers of odd index. LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 (using Blair Kelly's data) Blair Kelly, Fibonacci and Lucas Factorizations Eric Weisstein's World of Mathematics, Lucas Number FORMULA a(n) = Sum{d|n and n/d odd} A086600(d) + 1 if 6|n, a Mobius-like transform MATHEMATICA Lucas[n_] := Fibonacci[n+1] + Fibonacci[n-1]; Table[Length[FactorInteger[Lucas[n]]], {n, 150}] PROG (PARI) a(n)=omega(fibonacci(n-1)+fibonacci(n+1)) \\ Charles R Greathouse IV, Sep 14 2015 (MAGMA) [#PrimeDivisors(Lucas(n)): n in [1..100]]; // Vincenzo Librandi, Jul 26 2017 CROSSREFS Cf. A000204 (Lucas numbers), A086599 (number of prime factors, counting multiplicity), A086600 (number of primitive prime factors). Cf. A053027, A053028, A053032. Sequence in context: A143323 A344234 A338912 * A211261 A344174 A336431 Adjacent sequences:  A086595 A086596 A086597 * A086599 A086600 A086601 KEYWORD hard,nonn AUTHOR T. D. Noe, Jul 24 2003 STATUS approved

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Last modified September 21 15:37 EDT 2021. Contains 347598 sequences. (Running on oeis4.)