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%I #14 Mar 08 2014 02:26:14
%S 0,2,5,7,13,11,15,44,53,46,59,23,43,278,191,143,79,119,187,62,47,221,
%T 214,1643,159,238,95,473,314,3583,671,474,958,3071,5719,215,1439,7423,
%U 1663,447,223,3695,4346,4318,12983,319,35069,5983,5471,8567,959,3067
%N The first row of Pascal's triangle having exactly n distinct squarefree numbers, or -1 if no such row exists.
%H A. Granville and O. Ramaré, <a href="http://www.dms.umontreal.ca/~andrew/PDF/ramare.pdf">Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients</a>, Mathematika 43 (1996), 73-107, <a href="http://dx.doi.org/10.1112/S0025579300011608">[DOI]</a>.
%t nn = 20; t = Table[-1, {nn}]; found = 0; n = -1; While[found < nn, n++; len = Length[Select[Binomial[n, Range[0, n/2]], SquareFreeQ[#] &]]; If[0 < len <= nn && t[[len]] == -1, t[[len]] = n; found++]]; t
%Y Cf. A064461, A238337.
%K nonn,more,hard
%O 1,2
%A _T. D. Noe_, Mar 05 2014
%E Extended by _T. D. Noe_, Mar 07 2014
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