

A038575


Number of prime factors of nth Fibonacci number, counted with multiplicity.


17



0, 0, 0, 1, 1, 1, 3, 1, 2, 2, 2, 1, 6, 1, 2, 3, 3, 1, 5, 2, 4, 3, 2, 1, 9, 3, 2, 4, 4, 1, 7, 2, 4, 3, 2, 3, 10, 3, 3, 3, 6, 2, 7, 1, 5, 5, 3, 1, 12, 3, 6, 3, 4, 2, 8, 4, 7, 5, 3, 2, 12, 2, 3, 5, 6, 3, 7, 3, 5, 5, 7, 2, 14, 2, 4, 6, 5, 4, 8, 2, 9, 7, 3, 1, 13, 4, 3, 4, 9, 2, 12, 5, 6, 4, 2, 6, 16, 4, 5, 6, 10, 2, 8
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OFFSET

0,7


COMMENTS

Row lengths of table A060441.  Reinhard Zumkeller, Aug 30 2014


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
Eric Weisstein's World of Mathematics, Fibonacci Number


FORMULA

For n > 0: a(n) = A001222(A000045(n)).  Reinhard Zumkeller, Aug 30 2014


EXAMPLE

a(12) = 6 because Fibonacci(12) = 144 = 2^4 * 3^2 has 6 prime factors.


MAPLE

with(numtheory):with(combinat):a:=proc(n) if n=0 then 0 else bigomega(fibonacci(n)) fi end: seq(a(n), n=0..102); # Zerinvary Lajos, Apr 11 2008


MATHEMATICA

Join[{0, 0}, Table[Plus@@(Transpose[FactorInteger[Fibonacci[n]]][[2]]), {n, 3, 102}]]
Join[{0}, PrimeOmega[Fibonacci[Range[110]]]] (* Harvey P. Dale, Apr 14 2018 *)


PROG

(Haskell)
a038575 n = if n == 0 then 0 else a001222 $ a000045 n
 Reinhard Zumkeller, Aug 30 2014
(PARI) a(n)=bigomega(fibonacci(n)) \\ Charles R Greathouse IV, Sep 14 2015


CROSSREFS

Cf. A022307 (number of distinct prime factors), A086597 (number of primitive prime factors).
Cf. also A001222, A000045, A060441.
Sequence in context: A236172 A139381 A225849 * A304302 A305516 A305182
Adjacent sequences: A038572 A038573 A038574 * A038576 A038577 A038578


KEYWORD

nonn


AUTHOR

Jeff Burch


STATUS

approved



