A059913 Triangle T(n,k) of numbers of n degree irreducible polynomials over GF(2) which have order A059912(n,k), k=1..A059499(n).

2, 1, 2, 1, 2, 6, 1, 2, 6, 18, 2, 4, 8, 16, 8, 48, 1, 2, 6, 30, 60, 2, 8, 176, 1, 2, 2, 2, 4, 6, 4, 6, 8, 12, 12, 24, 24, 36, 48, 144, 630, 3, 6, 18, 378, 756, 10, 12, 60, 300, 1800, 16, 32, 64, 128, 256, 512, 1024, 2048, 7710, 1, 1, 2, 6, 6, 6, 8, 12, 18, 24

Offset: 1

Author

Vladeta Jovovic, Feb 09 2001

Keywords

• easy
• nonn
• tabf

Comments

Row sums give A001037.

Examples

			There are 9 (cf. A001037) irreducible polynomials of degree 6 over GF(2): 1 of order 9, 2 of order 21 and 6 of order 63 (cf. A059912).
Triangle T(n,k) begins:
  2;
  1;
  2;
  1,  2;
  6;
  1,  2,   6;
  18;
  2,  4,   8, 16;
  8, 48;
  1,  2,   6, 30, 60;
  2,  8, 176;
  ...
		

Links

• Alois P. Heinz, Rows n = 1..71, flattened

Crossrefs

Cf. A058943, A059478, A059499, A001037, A059912, A000010.

Programs

Mathematica

Prepend[Table[Map[EulerPhi[#]/n &, Complement[Divisors[2^n - 1],Union[Flatten[Table[Divisors[2^k - 1], {k, 1, n - 1}]]]]], {n, 2,20}], {2}] // Grid (* Geoffrey Critzer, Dec 02 2019 *)

Formula

T(n,k) = phi(A059912(n,k))/n, where phi = Euler totient function A000010.