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A061305
Squarefree Fibonacci numbers.
10
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
OFFSET
1,3
COMMENTS
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
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1080 (terms 1..200 from Zak Seidov)
FORMULA
Set difference of A000045 and A061899. a(n) = A000045(A037918(n)). - R. J. Mathar, Feb 16 2010
EXAMPLE
55 = 5 * 11 is a squarefree Fibonacci number.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Intersection of A000045 and A005117.
Sequence in context: A173830 A224223 A238497 * A177374 A142881 A163159
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Apr 26 2001
EXTENSIONS
More terms from Asher Auel, May 14 2001
Mathematica updated by Jean-François Alcover, Jul 04 2013
STATUS
approved