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A086598
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Number of distinct prime factors in Lucas(n).
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3
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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; internal format)
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OFFSET
| 1,6
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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.
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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
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FORMULA
| a(n) = Sum{d|n and n/d odd} A086600(d) + 1 if 6|n, a Mobius-like transform
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MATHEMATICA
| Lucas[n_] := Fibonacci[n+1] + Fibonacci[n-1]; Table[Length[FactorInteger[Lucas[n]]], {n, 150}]
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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: A035170 A111949 A143323 * A074746 A133188 A008612
Adjacent sequences: A086595 A086596 A086597 * A086599 A086600 A086601
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KEYWORD
| hard,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Jul 24 2003
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