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Numbers that match polynomials not irreducible over the nonnegative integers.
3

%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