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A111079
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GCD(F(n), product{k|n,k<n} F(k)), where F(k) is k-th Fibonacci number.
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1, 1, 1, 1, 1, 2, 1, 3, 2, 5, 1, 48, 1, 13, 10, 21, 1, 136, 1, 165, 26, 89, 1, 2016, 5, 233, 34, 1131, 1, 26840, 1, 987, 178, 1597, 65, 139536, 1, 4181, 466, 47355, 1, 1269736, 1, 53133, 10370, 28657, 1, 4358592, 13, 825275, 3194, 364179, 1, 14927768, 445
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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EXAMPLE
| The proper divisors of 16 are 1, 2, 4, 8. So a(16) = GCD(F(16), F(1)*F(2)*F(4)*F(8)) = GCD(987, 1*1*3*21) = 21.
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MAPLE
| with(combinat): with(numtheory): a:=proc(n) local div: div:=divisors(n): gcd(fibonacci(n), product(fibonacci(div[j]), j=1..tau(n)-1)): end: seq(a(n), n=1..65); (Deutsch)
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MATHEMATICA
| f[n_] := GCD[Fibonacci[n], Times @@ Fibonacci /@ Most[Divisors[n]]]; Table[ f[n], {n, 55}] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A000045.
Sequence in context: A181363 A105800 A105602 * A165006 A134735 A050360
Adjacent sequences: A111076 A111077 A111078 * A111080 A111081 A111082
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Oct 11 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 12 2005
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