

A080345


a(n) is the number of prime factors in Fibonacci(prime(n)); that is, in the Fibonacci number whose index is the nth prime.


4



0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 2, 2, 2, 3, 2, 2, 2, 1, 2, 4, 2, 3, 2, 2, 2, 2, 1, 1, 3, 4, 2, 4, 4, 2, 2, 3, 3, 2, 2, 4, 2, 4, 4, 2, 5, 3, 4, 3, 2, 3, 3, 4, 2, 2, 3, 4, 2, 4, 4, 4, 3, 2, 3, 5, 4, 2, 1, 7, 5, 4, 3, 3, 2, 2, 4, 3, 4, 1, 1, 5, 5, 1, 3, 5, 3, 2, 3, 4, 3, 4, 6, 1, 3, 4, 3
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OFFSET

1,8


COMMENTS

In all known examples, Fibonacci(prime(n)) is squarefree, in which case a(n) is welldefined, i.e., the number of distinct prime factors equals the total number of prime factors. But if for some n, Fibonacci(prime(n)) has a repeated prime factor, then a(n) is not welldefined.  Jonathan Sondow, Oct 22 2015


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..222 (terms 1..168 from T. D. Noe)
Blair Kelly, Fibonacci and Lucas Factorizations


FORMULA

a(n) = A001221(A000045(A000040(n))).  Michel Marcus, Oct 22 2015


EXAMPLE

a(12) = 3 because the 12th prime is 37 and Fibonacci(37) = 24157817 = 73 * 149 * 2221 has 3 prime factors.  clarified by Jonathan Sondow, Oct 21 2015


MATHEMATICA

Table[Length[FactorInteger[Fibonacci[Prime[n]]]], {n, 60}]
PrimeNu[Fibonacci[Prime[Range[100]]]] (* Harvey P. Dale, Mar 13 2016 *)


PROG

(PARI) a(n) = omega(fibonacci(prime(n))); \\ Michel Marcus, Oct 22 2015


CROSSREFS

Cf. A001605, A014600, A022307.
Sequence in context: A204030 A234503 A236325 * A285202 A004737 A255616
Adjacent sequences: A080342 A080343 A080344 * A080346 A080347 A080348


KEYWORD

hard,nonn


AUTHOR

T. D. Noe, Feb 16 2003


STATUS

approved



