Search: id:A086598
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%I A086598
%S A086598 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,
%T A086598 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,
%U A086598 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
%N A086598 Number of distinct prime factors in Lucas(n).
%C A086598 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.
%H A086598 T. D. Noe, <a href="b086598.txt">Table of n, a(n) for n=1..1000</a> (using 
               Blair Kelly's data)
%H A086598 Blair Kelly, <a href="http://home.att.net/~blair.kelly/mathematics/fibonacci/
               ">Fibonacci and Lucas Factorizations</a>
%H A086598 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LucasNumber.html">Lucas Number</a>
%F A086598 a(n) = Sum{d|n and n/d odd} A086600(d) + 1 if 6|n, a Mobius-like transform
%t A086598 Lucas[n_] := Fibonacci[n+1] + Fibonacci[n-1]; Table[Length[FactorInteger[Lucas[n]]], 
               {n, 150}]
%Y A086598 Cf. A000204 (Lucas numbers), A086599 (number of prime factors, counting 
               multiplicity), A086600 (number of primitive prime factors).
%Y A086598 Cf. A053027, A053028, A053032.
%Y A086598 Sequence in context: A035170 A111949 A143323 this_sequence A074746 A133188 
               A008612
%Y A086598 Adjacent sequences: A086595 A086596 A086597 this_sequence A086599 A086600 
               A086601
%K A086598 hard,nonn
%O A086598 1,6
%A A086598 T. D. Noe (noe(AT)sspectra.com), Jul 24 2003

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