This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A206284 Numbers that match irreducible polynomials over the nonnegative integers. 23
 3, 6, 9, 10, 12, 18, 20, 22, 24, 27, 28, 30, 36, 40, 42, 44, 46, 48, 50, 52, 54, 56, 60, 66, 68, 70, 72, 76, 80, 81, 88, 92, 96, 98, 100, 102, 104, 108, 112, 114, 116, 118, 120, 124, 126, 130, 132, 136, 140, 144, 148, 150, 152, 154, 160, 162, 164, 168, 170 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS After p(1) which encodes 0-polynomial, each n > 1 corresponds with a polynomial having nonnegative integer coefficients determined by the prime factorization of n. Write n = p(1)^e(1) * p(2)^e(2) * ... * p(k)^e(k). The matching polynomial is then p(n,x) = e(1) + e(2)x + e(3)x^2 + ... + e(k)x^k. Identities:   p(m*n,x) = p(m,x) + p(n,x),   p(m*n,x) = p(gcd(m,n),x) + p(lcm(m,n),x),   p(m+n,x) = p(gcd(m,n),x) + p((m+n)/gcd(m,n),x), so that if A003057 is read as a square matrix, then   p(A003057,x) = p(A003989,x) + p(A106448,x). Apart from powers of 3, all terms are even. - Charles R Greathouse IV, Feb 11 2012 Contains 2*p^m and p*2^m if p is an odd prime and m is in A052485. - Robert Israel, Oct 09 2016 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10566 EXAMPLE Polynomials having nonnegative integer coefficients are matched to the positive integers as follows:    n    p[n,x]    irreducible   ---------------------------    1    0         no    2    1         no    3    x         yes    4    2         no    5    x^2       no    6    1+x       yes    7    x^3       no    8    3         no    9    2x        yes   10    1+x^2     yes MAPLE P:= n -> add(f*x^(numtheory:-pi(f)-1), f =  ifactors(n)): select(irreduc @ P, [\$1..200]); # Robert Israel, Oct 09 2016 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, v]      (* A206285 *) PROG (PARI) is(n)=my(f=factor(n)); polisirreducible(sum(i=1, #f[, 1], f[i, 2]*'x^primepi(f[i, 1]-1))) \\ Charles R Greathouse IV, Feb 12 2012 CROSSREFS Cf. A052485, A206285, A206296. Positions of ones in A277322. Terms of A277318 form a proper subset of this sequence. Cf. also A277316. Sequence in context: A113502 A229307 A061904 * A268328 A247575 A289130 Adjacent sequences:  A206281 A206282 A206283 * A206285 A206286 A206287 KEYWORD nonn AUTHOR Clark Kimberling, Feb 05 2012 EXTENSIONS Comment section edited and typos corrected by Antti Karttunen, Oct 09 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)