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

1,3

Links

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

Example

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

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 *)

Crossrefs

Cf. A048276, A048277, A048278.

Sequence in context: A274188 A335437 A034040 * A250656 A072836 A373265

Adjacent sequences: A048276 A048277 A048278 * A048280 A048281 A048282

Keyword

nonn

Author

Labos Elemer

Extensions

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

Status

approved