This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A037918 #38 Jul 02 2025 16:01:56 %S A037918 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, %T A037918 32,33,34,35,37,38,39,40,41,43,44,45,46,47,49,51,52,53,55,57,58,59,61, %U A037918 62,63,64,65,67,68,69,70,71,73,74,76,77,79,80,81,82,83,85,86,87,88,89,92 %N A037918 Numbers n such that the Fibonacci number F(n) is squarefree. %H A037918 Amiram Eldar, <a href="/A037918/b037918.txt">Table of n, a(n) for n = 1..1080</a> (terms 1..765 from T. D. Noe, based on Kelly's table) %H A037918 Blair Kelly, <a href="http://mersennus.net/fibonacci//f1000.txt">Fibonacci Factorizations</a> %H A037918 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number.</a> %e A037918 10 is in the sequence because F(10) = 55, which is squarefree since 55 = 5 * 11. %e A037918 11 is in the sequence because F(11) = 89, which is prime and therefore also squarefree. %e A037918 12 is not in the sequence because F(12) = 144 = 2^4 * 3^2 = 12^2. %t A037918 Select[Range[100], SquareFreeQ[Fibonacci[#]] &] (* _Vladimir Joseph Stephan Orlovsky_, Jul 01 2011 *) %t A037918 Select[Range[100], MoebiusMu[Fibonacci[#]] != 0 &] (* _Alonso del Arte_, Jan 26 2014 *) %o A037918 (PARI) select(n->(0!=moebius(fibonacci(n))),vector(100,j,j)) \\ _Joerg Arndt_, Jan 28 2014 %o A037918 (Magma) [n: n in [1..100] | IsSquarefree(Fibonacci(n))]; // _Vincenzo Librandi_, Jun 01 2015 %Y A037918 Cf. A000045, A037917. %K A037918 nonn %O A037918 1,2 %A A037918 _N. J. A. Sloane_, _Marc LeBrun_ %E A037918 More terms from _James Sellers_, May 29 2000