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A206285 Numbers that match polynomials not irreducible over the nonnegative integers. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Complement of A206284.

LINKS

Table of n, a(n) for n=1..67.

EXAMPLE

(See the example at A206284.)

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 *)

CROSSREFS

Cf. A206285, A206331.

Sequence in context: A188298 A289129 A290334 * A229303 A262978 A112886

Adjacent sequences:  A206282 A206283 A206284 * A206286 A206287 A206288

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 05 2012

STATUS

approved

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Last modified October 18 05:18 EDT 2019. Contains 328146 sequences. (Running on oeis4.)