

A037918


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


15



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
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OFFSET

1,2


LINKS

T. D. Noe, Table of n, a(n) for n=1..765 (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



