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A038575 Number of prime factors of n-th Fibonacci number, counted with multiplicity. 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

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

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000 (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 A291047 A033178

Adjacent sequences:  A038572 A038573 A038574 * A038576 A038577 A038578

KEYWORD

nonn

AUTHOR

Jeff Burch

STATUS

approved

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Last modified May 22 08:14 EDT 2018. Contains 304405 sequences. (Running on oeis4.)