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%I #9 Apr 17 2018 18:06:42
%S 1,1,2,5,13,55,89,233,377,610,1597,4181,10946,17711,28657,121393,
%T 514229,1346269,3524578,5702887,9227465,24157817,39088169,63245986,
%U 165580141,433494437,1836311903,2971215073,20365011074,53316291173
%N Squarefree Fibonacci numbers whose indices are also squarefree.
%e Fib(10)=55 is there because both 10 and 55 are squarefree.
%p with(combinat, fibonacci): fib_supM_dsk := proc(n); if (numtheory[issqrfree](n)='true') then if (numtheory[issqrfree](fibonacci(n))='true') then RETURN(fibonacci(n)); fi; fi; end: seq(fib_supM_dsk(i), i=1..100);
%t Select[With[{nn=70},Thread[{Range[nn],Fibonacci[Range[nn]]}]], AllTrue[#, SquareFreeQ]&][[All,2]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Apr 17 2018 *)
%Y Cf. A000045, A005117, A061305, A075739.
%K easy,nonn
%O 1,3
%A _Jani Melik_, Oct 07 2002
%E Edited by _Don Reble_, Nov 05 2005