Numbers n for which a record number of numbers binomial(n,m) are squarefree, where m <= n/2.
0, 2, 5, 7, 11, 15, 23, 43, 47, 95, 215, 223, 239, 479, 3967, 33119, 84319
1
Note that only the terms 15, 95, and 215 are composite. Sequence S001078 gives the number of squarefree terms for each n. Is it possible that this sequence is finite?
T. D. Noe, Plot of 16 terms
Wikipedia, Binomial coefficient
(Mma) mx = -1; t = {}; Do[temp = Length[Select[Binomial[n, Range[0, n/2]], SquareFreeQ[#] &]]; If[temp > mx, mx = temp; AppendTo[t, {n, mx}]], {n, 0, 500}]; Transpose[t][[1]]
nonn,more
T. D. Noe, Jan 25 2018