The squareful part of the n-th Lucas number.
1, 1, 1, 4, 1, 1, 9, 1, 1, 4, 1, 1, 1, 1, 1, 4, 1, 1, 27, 1, 1, 4, 1, 1, 1, 1, 1, 4, 49, 1, 9, 1, 1, 4, 1, 1, 1, 1, 1, 4, 1, 1, 9, 1, 1, 4, 1, 1, 1, 1, 1, 4, 1, 1, 81, 121, 1, 4, 1, 1, 1, 1, 1, 4, 1, 1, 9, 1, 1, 4, 1, 1, 1, 1, 1, 4, 1, 1, 9, 1, 1, 4, 1, 1, 49, 1
0
Note that the squareful part is much smaller than Lucas(n).
T. D. Noe, Plot of 501 terms
T. D. Noe, Table of 501 terms
Eric W. Weisstein, MathWorld: Lucas Number
(Mma) Table[f = Select[FactorInteger[LucasL[n], Automatic], #[[2]] > 1 &]; If[f == {}, 1, Times @@ Power @@ Transpose[f]], {n, Range[0, 200]}]
Cf. S000323, S000324, S000326.
nonn
T. D. Noe, Nov 11 2014