A037918 Numbers n such that the Fibonacci number F(n) is squarefree.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 76, 77, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 92

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..1080 (terms 1..765 from T. D. Noe, based on Kelly's table)

Blair Kelly, Fibonacci Factorizations

Eric Weisstein's World of Mathematics, Fibonacci Number.

Example

10 is in the sequence because F(10) = 55, which is squarefree since 55 = 5 * 11.
11 is in the sequence because F(11) = 89, which is prime and therefore also squarefree.
12 is not in the sequence because F(12) = 144 = 2^4 * 3^2 = 12^2.

Mathematica

Select[Range[100], SquareFreeQ[Fibonacci[#]] &] (* Vladimir Joseph Stephan Orlovsky, Jul 01 2011 *)
Select[Range[100], MoebiusMu[Fibonacci[#]] != 0 &] (* Alonso del Arte, Jan 26 2014 *)

Prog

(PARI) select(n->(0!=moebius(fibonacci(n))), vector(100, j, j)) \\ Joerg Arndt, Jan 28 2014
(Magma) [n: n in [1..100] | IsSquarefree(Fibonacci(n))]; // Vincenzo Librandi, Jun 01 2015

Crossrefs

Cf. A000045, A037917.

Sequence in context: A248910 A254278 A204878 * A043091 A031943 A023800

Adjacent sequences: A037915 A037916 A037917 * A037919 A037920 A037921

Keyword

nonn

Author

N. J. A. Sloane, Marc LeBrun

Extensions

More terms from James A. Sellers, May 29 2000

Status

approved