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A080345
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a(n) is the number of prime factors in Fibonacci(prime(n)); that is, in the Fibonacci number whose index is the n-th prime.
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4
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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
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1,8
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COMMENTS
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In all known examples, Fibonacci(prime(n)) is squarefree, in which case a(n) is well-defined, 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 well-defined. - Jonathan Sondow, Oct 22 2015
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LINKS
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FORMULA
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EXAMPLE
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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
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MATHEMATICA
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Table[Length[FactorInteger[Fibonacci[Prime[n]]]], {n, 60}]
PrimeNu[Fibonacci[Prime[Range[100]]]] (* Harvey P. Dale, Mar 13 2016 *)
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PROG
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(PARI) a(n) = omega(fibonacci(prime(n))); \\ Michel Marcus, Oct 22 2015
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CROSSREFS
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KEYWORD
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hard,nonn
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AUTHOR
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STATUS
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approved
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