A075738 Squarefree Fibonacci numbers whose indices are also squarefree.
1, 1, 2, 5, 13, 55, 89, 233, 377, 610, 1597, 4181, 10946, 17711, 28657, 121393, 514229, 1346269, 3524578, 5702887, 9227465, 24157817, 39088169, 63245986, 165580141, 433494437, 1836311903, 2971215073, 20365011074, 53316291173
Offset: 1
Examples
Fib(10)=55 is there because both 10 and 55 are squarefree.
Programs
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Maple
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);
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Mathematica
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 *)
Extensions
Edited by Don Reble, Nov 05 2005