A048279 Values of n for which no values of C(n,k) except k=0 and k=n are squarefree.

0, 1, 9, 16, 18, 27, 32, 36, 48, 49, 50, 56, 64, 72, 80, 81, 96, 98, 99, 100, 108, 112, 121, 126, 128, 135, 136, 144, 147, 148, 153, 162, 169, 171, 175, 176, 180, 192, 196, 198, 200, 216, 225, 243, 244, 245, 248, 250, 252, 256, 264, 272, 276, 288, 289, 294, 300

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			n=9, C(n,k) = (1),9,36,84,126,126,84,36,9,(1); all values include squares.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A048276, A048277, A048278.

Programs

Mathematica

f[n_] := (c = 0; k = 1; While[k < n, If[ Union[ Transpose[ FactorInteger[ Binomial[n, k]]] [[2]]] [[ -1]] > 1, c++ ]; k++ ]; c); Select[Range[150], f[ # ] == # - 1 &]
a[ n_] := If[ n < 2, 0, Module[ {c = 1, k = 1}, While[ c < n, If[ {} == Select[ Table[ Binomial[k, i], {i, k - 1}], SquareFreeQ], c++]; k++]; k - 1]]; (* Michael Somos, Mar 07 2014 *)
Join[{0,1},Select[Range[3,300],NoneTrue[Binomial[#,Range[2,#-1]], SquareFreeQ] &]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 29 2019 *)

Extensions

More terms from Robert G. Wilson v, Oct 02 2001