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

1,1

Comments

Row sums give A001037.

Links

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

Formula

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

Example

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;
  ...

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 *)

Crossrefs

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

Sequence in context: A020733 A210700 A215745 * A329602 A083273 A353398

Adjacent sequences: A059910 A059911 A059912 * A059914 A059915 A059916

Keyword

easy,nonn,tabf

Author

Vladeta Jovovic, Feb 09 2001

Status

approved