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
Keywords
Examples
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.
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.
Programs
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Magma
[n: n in [1..100] | IsSquarefree(Fibonacci(n))]; // Vincenzo Librandi, Jun 01 2015
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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 *)
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PARI
select(n->(0!=moebius(fibonacci(n))),vector(100,j,j)) \\ Joerg Arndt, Jan 28 2014
Extensions
More terms from James Sellers, May 29 2000