id:A086598 - OEIS Search Results

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Number of distinct prime factors in Lucas(n).

+0
3

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; listen)

	OFFSET	`1,6`
	COMMENT	`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}]`
	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 this_sequence A074746 A133188 A008612` `Adjacent sequences: A086595 A086596 A086597 this_sequence A086599 A086600 A086601`
	KEYWORD	`hard,nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Jul 24 2003`

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.

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