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

Author

Amarnath Murthy, Apr 26 2001

Keywords

• nonn
• easy

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

Examples

			55 = 5 * 11 is a squarefree Fibonacci number.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1080 (terms 1..200 from Zak Seidov)

Crossrefs

Intersection of A000045 and A005117.

Programs

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 *)

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

Formula

Set difference of A000045 and A061899. a(n) = A000045(A037918(n)). - R. J. Mathar, Feb 16 2010

Extensions

More terms from Asher Auel, May 14 2001

Mathematica updated by Jean-François Alcover, Jul 04 2013