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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). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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, A059914-A059916, A000010. Sequence in context: A020733 A210700 A215745 * A329602 A083273 A193163 Adjacent sequences:  A059910 A059911 A059912 * A059914 A059915 A059916 KEYWORD easy,nonn,tabf AUTHOR Vladeta Jovovic, Feb 09 2001 STATUS approved

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Last modified July 28 13:45 EDT 2021. Contains 346334 sequences. (Running on oeis4.)