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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
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)
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
Sequence in context: A248910 A254278 A204878 * A043091 A031943 A023800
KEYWORD
nonn
EXTENSIONS
More terms from James A. Sellers, May 29 2000
STATUS
approved