Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Sep 29 2019 10:25:02
%S 0,1,9,16,18,27,32,36,48,49,50,56,64,72,80,81,96,98,99,100,108,112,
%T 121,126,128,135,136,144,147,148,153,162,169,171,175,176,180,192,196,
%U 198,200,216,225,243,244,245,248,250,252,256,264,272,276,288,289,294,300
%N Values of n for which no values of C(n,k) except k=0 and k=n are squarefree.
%H T. D. Noe, <a href="/A048279/b048279.txt">Table of n, a(n) for n = 1..1000</a>
%e n=9, C(n,k) = (1),9,36,84,126,126,84,36,9,(1); all values include squares.
%t 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 &]
%t 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 *)
%t 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 *)
%Y Cf. A048276, A048277, A048278.
%K nonn
%O 1,3
%A _Labos Elemer_
%E More terms from _Robert G. Wilson v_, Oct 02 2001