OFFSET
0,9
COMMENTS
Although every prime divides some Fibonacci number, this is not true for the Lucas numbers. Exactly 1/3 of all primes do not divide any Lucas number. See Lagarias and Moree for more details. - Jonathan Vos Post, Dec 06 2006
First occurrence of k: 0, 3, 8, 15, 20, 30, 40, 70, 60, 80, 90, 140, 176, 120, 168, 180, 324, 252, 240, 378, ..., . - Robert G. Wilson v, Dec 10 2006 [Other than 0, this is sequence A060320. - Jon E. Schoenfield, Dec 30 2016]
Row lengths of table A060442. - Reinhard Zumkeller, Aug 30 2014
If k properly divides n then a(n) >= a(k) + 1, except for a(6) = a(3) = 1. - Robert Israel, Aug 18 2015
REFERENCES
Alfred Brousseau, Fibonacci and Related Number Theoretic Tables, The Fibonacci Association, 1972, pages 1-8.
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..1408 (terms 0..1000 from T. D. Noe derived from Kelly's data)
Blair Kelly, Fibonacci and Lucas Factorizations
J. C. Lagarias, The set of primes dividing the Lucas numbers has density 2/3, Pacific J. Math., 118. No. 2, (1985), 449-461.
J. C. Lagarias, Errata to: The set of primes dividing the Lucas numbers has density 2/3, Pacific J. Math., 162, No. 2, (1994), 393-396.
Hisanori Mishima, WIFC (World Integer Factorization Center), Fibonacci numbers (n = 1 to 100, n = 101 to 200, n = 201 to 300, n = 301 to 400, n = 401 to 480).
Pieter Moree, Counting Divisors of Lucas Numbers, Pacific J. Math, Vol. 186, No. 2, 1998, pp. 267-284.
Eric Weisstein's World of Mathematics, Fibonacci Number
FORMULA
MATHEMATICA
Table[Length[FactorInteger[Fibonacci[n]]], {n, 150}]
PROG
(PARI) a(n)=omega(fibonacci(n)) \\ Charles R Greathouse IV, Feb 03 2014
(Haskell)
a022307 n = if n == 0 then 0 else a001221 $ a000045 n
-- Reinhard Zumkeller, Aug 30 2014
(Magma) [0] cat [#PrimeDivisors(Fibonacci(n)): n in [1..100]]; // Vincenzo Librandi, Jul 26 2017
CROSSREFS
Cf. A038575 (number of prime factors, counting multiplicity), A086597 (number of primitive prime factors).
Cf. A060320. - Jon E. Schoenfield, Dec 30 2016
KEYWORD
nonn
AUTHOR
STATUS
approved