The number of numbers for which binomial(n,m) is squarefree, where n is in S001077 and m <= n/2.

1, 2, 3, 4, 6, 7, 12, 13, 21, 27, 36, 41, 56, 74, 91, 94

1

It is somewaht surprising that so few of the numbers binomial(n,m) are squarefree. Is it possible that this sequence is finite? The values of m are given in S001079.

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][[2]]

Cf. A238337, S001077, S001079.

nonn,more

T. D. Noe, Jan 25 2018