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A061305
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Squarefree Fibonacci numbers.
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10
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1, 1, 2, 3, 5, 13, 21, 34, 55, 89, 233, 377, 610, 987, 1597, 4181, 6765, 10946, 17711, 28657, 121393, 196418, 317811, 514229, 1346269, 2178309, 3524578, 5702887, 9227465, 24157817, 39088169, 63245986, 102334155, 165580141, 433494437, 701408733, 1134903170, 1836311903
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OFFSET
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1,3
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COMMENTS
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Union of A074691 and A075735. - R. J. Mathar, Feb 06 2010
About 60% of entries are of the form 4k+1; 20% are of the form 4k+2; 20% are of the form 4k+3. Obviously no term is divisible by 4. - Carmine Suriano, Feb 27 2014
Contains A030426 as a subsequence unless there exist Wall-Sun-Sun primes. - Max Alekseyev, Jan 04 2018
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..1080 (terms 1..200 from Zak Seidov)
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FORMULA
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Set difference of A000045 and A061899. a(n) = A000045(A037918(n)). - R. J. Mathar, Feb 16 2010
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EXAMPLE
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55 = 5 * 11 is a squarefree Fibonacci number.
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MATHEMATICA
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a={}; Do[f=Fibonacci[n]; If[SquareFreeQ[f], AppendTo[a, f]], {n, 1, 50}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 22 2008 *)
Select[Fibonacci[Range[50]], SquareFreeQ] (* Harvey P. Dale, Aug 26 2021 *)
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PROG
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(PARI) { n=0; g=0; f=1; for (i=1, 500, if (issquarefree(g), write("b061305.txt", n++, " ", g)); if (n==200, break); s=f; f+=g; g=s ) } \\ Harry J. Smith, Jul 21 2009
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CROSSREFS
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Intersection of A000045 and A005117.
Sequence in context: A173830 A224223 A238497 * A177374 A142881 A163159
Adjacent sequences: A061302 A061303 A061304 * A061306 A061307 A061308
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KEYWORD
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nonn,easy
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AUTHOR
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Amarnath Murthy, Apr 26 2001
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EXTENSIONS
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More terms from Asher Natan Auel (auela(AT)reed.edu), May 14 2001
Mathematica updated by Jean-François Alcover, Jul 04 2013
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STATUS
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approved
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