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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).

%I A059913 #19 Jun 03 2022 07:43:05
%S A059913 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,
%T A059913 6,8,12,12,24,24,36,48,144,630,3,6,18,378,756,10,12,60,300,1800,16,32,
%U A059913 64,128,256,512,1024,2048,7710,1,1,2,6,6,6,8,12,18,24
%N 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).
%C A059913 Row sums give A001037.
%H A059913 Alois P. Heinz, <a href="/A059913/b059913.txt">Rows n = 1..71, flattened</a>
%F A059913 T(n,k) = phi(A059912(n,k))/n, where phi = Euler totient function A000010.
%e A059913 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).
%e A059913 Triangle T(n,k) begins:
%e A059913   2;
%e A059913   1;
%e A059913   2;
%e A059913   1,  2;
%e A059913   6;
%e A059913   1,  2,   6;
%e A059913   18;
%e A059913   2,  4,   8, 16;
%e A059913   8, 48;
%e A059913   1,  2,   6, 30, 60;
%e A059913   2,  8, 176;
%e A059913   ...
%t A059913 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 *)
%Y A059913 Cf. A058943, A059478, A059499, A001037, A059912, A000010.
%K A059913 easy,nonn,tabf
%O A059913 1,1
%A A059913 _Vladeta Jovovic_, Feb 09 2001