A061305 Squarefree Fibonacci numbers.

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

Adjacent sequences: A061302 A061303 A061304 * A061306 A061307 A061308

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