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A258575 Numbers n such that Lucas(n)-Fibonacci(n) is squarefree.

%I A258575 #23 Sep 08 2022 08:46:12
%S A258575 0,2,3,5,6,8,9,11,12,14,15,17,18,20,21,23,24,27,29,30,32,33,35,36,38,
%T A258575 39,41,42,44,45,47,48,50,53,54,56,59,60,62,63,65,66,68,69,71,72,74,75,
%U A258575 77,78,80,81,83,84,86,87,89,90,93,95,96,98,99,102,104,105
%N A258575 Numbers n such that Lucas(n)-Fibonacci(n) is squarefree.
%C A258575 These numbers belong to the sequence A007494 (see _Chai Wah Wu_ argumentation in A258574).
%C A258575 Also numbers n such that 2*Fibonacci(n-1) is squarefree. [_Bruno Berselli_, Jun 05 2015]
%C A258575 A258575(n) = A258574(n+1)-1. - _Chai Wah Wu_, Jun 09 2015
%t A258575 Select[Range[0, 200], SquareFreeQ[LucasL[#] - Fibonacci[#]] &]
%o A258575 (Magma) [0] cat [n: n in [2..150] | IsSquarefree(Lucas(n)-Fibonacci(n))];
%o A258575 (Sage) [n for n in (0..110) if is_squarefree(2*fibonacci(n-1))] # _Bruno Berselli_, Jun 05 2015
%Y A258575 Cf. A000032, A000045, A005117, A007494, A037918, A118658, A258574.
%K A258575 nonn,easy,less
%O A258575 1,2
%A A258575 _Vincenzo Librandi_, Jun 04 2015
%E A258575 Name corrected by _Bruno Berselli_, Jun 05 2015