The index of Lucas numbers that are not squarefree.
3, 6, 9, 15, 18, 21, 27, 28, 30, 33, 39, 42, 45, 51, 54, 55, 57, 63, 66, 69, 75, 78, 81, 84, 87, 90, 93, 99, 102, 105, 111, 114, 117, 123, 126, 129, 135, 138, 140, 141, 147, 150, 153, 159, 162, 165, 171, 174, 177, 183, 186, 189, 195, 196, 198, 201, 203, 207
1
It appears that about 29% of Lucas numbers are not squarefree.
T. D. Noe, Plot of 100 terms
T. D. Noe, Table of 100 terms
Pierre Le Boudec, On the distribution of squarefree integers in arithmetic progressions, arXiv 1411.2360 (Nov 10 2014)
Eric W. Weisstein, MathWorld: Lucas Number
(Mma) Select[Range[200], ! SquareFreeQ[LucasL[#]] &]
Cf. S000324.
nonn
T. D. Noe, Nov 11 2014