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A059913
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Triangle T(n,k) of numbers of n degree irreducible polynomials over GF(2) which have order A059912(n,k), k=1..A059499(n).
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2
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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T(n,k) = phi(A059912(n,k))/n, where phi = Euler totient function A000010.
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EXAMPLE
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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;
...
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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STATUS
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approved
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