%I #8 Mar 30 2012 18:58:12
%S 1,2,4,5,7,8,11,13,14,15,16,17,19,21,23,25,26,29,31,32,33,34,35,37,38,
%T 39,41,43,45,47,49,51,53,55,57,58,59,61,62,63,64,65,67,69,71,73,74,75,
%U 77,78,79,82,83,84,85,86,87,89,90,91,93,94,95,97,99,101,103
%N Numbers that match polynomials not irreducible over the nonnegative integers.
%C Complement of A206284.
%e (See the example at A206284.)
%t b[n_] := Table[x^k, {k, 0, n}];
%t f[n_] := f[n] = FactorInteger[n]; z = 400;
%t t[n_, m_, k_] := If[PrimeQ[f[n][[m, 1]]] && f[n][[m, 1]]
%t == Prime[k], f[n][[m, 2]], 0];
%t u = Table[Apply[Plus,
%t Table[Table[t[n, m, k], {k, 1, PrimePi[n]}], {m, 1,
%t Length[f[n]]}]], {n, 1, z}];
%t p[n_, x_] := u[[n]].b[-1 + Length[u[[n]]]]
%t Table[p[n, x], {n, 1, z/4}]
%t v = {}; Do[n++; If[IrreduciblePolynomialQ[p[n, x]],
%t AppendTo[v, n]], {n, z/2}]; v (* A206284 *)
%t Complement[Range[200], v] (* A206285 *)
%Y Cf. A206285, A206331.
%K nonn
%O 1,2
%A _Clark Kimberling_, Feb 05 2012