The squareful part of the n-th Fibonacci number.
1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 144, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 288, 25, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 432, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 576, 1, 25, 1, 1, 1, 8, 1, 49, 1, 1, 1, 144, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 864, 1, 1, 25, 1, 1, 8, 1, 1, 1, 1
1
Note that the squareful part is much smaller than Fib(n).
T. D. Noe, Plot of 500 terms
T. D. Noe, Table of 500 terms
Eric W. Weisstein, MathWorld: Fibonacci Number
(Mma) Table[f = Select[FactorInteger[Fibonacci[n], Automatic], #[[2]] > 1 &]; If[f == {}, 1, Times @@ Power @@ Transpose[f]], {n, Range[200]}]
Cf. A037917 (index of squareful Fibonacci numbers), S000325.
nonn
T. D. Noe, Nov 11 2014