A206285 Numbers that match polynomials not irreducible over the nonnegative integers.

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, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 69, 71, 73, 74, 75, 77, 78, 79, 82, 83, 84, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 99, 101, 103

Offset: 1

Author

Clark Kimberling, Feb 05 2012

Keywords

• nonn

Comments

Complement of A206284.

Examples

			(See the example at A206284.)
		

Crossrefs

Cf. A206285, A206331.

Programs

Mathematica

b[n_] := Table[x^k, {k, 0, n}];
f[n_] := f[n] = FactorInteger[n]; z = 400;
t[n_, m_, k_] := If[PrimeQ[f[n][[m, 1]]] && f[n][[m, 1]]
== Prime[k], f[n][[m, 2]], 0];
u = Table[Apply[Plus,
    Table[Table[t[n, m, k], {k, 1, PrimePi[n]}], {m, 1,
      Length[f[n]]}]], {n, 1, z}];
p[n_, x_] := u[[n]].b[-1 + Length[u[[n]]]]
Table[p[n, x], {n, 1, z/4}]
v = {}; Do[n++; If[IrreduciblePolynomialQ[p[n, x]],
AppendTo[v, n]], {n, z/2}]; v  (* A206284 *)
Complement[Range[200], v]      (* A206285 *)