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A346019
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Number of n X n invertible matrices over GF(2) that have order 2^n-1.
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1
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1, 2, 48, 2688, 1935360, 1919877120, 23222833643520, 335564785519165440, 65717007596073359769600, 21492090164219831579049984000, 66041307304745851496871108594892800, 226523509196861965428709270554756199219200, 16622838761287803491875715175557341313583022080000
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OFFSET
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1,2
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COMMENTS
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Equivalently, a(n) is the number of n X n matrices over GF(2) whose characteristic polynomial is primitive.
2^n - 1 is the greatest order that a matrix in the general linear group GL_n(F_2) can have.
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LINKS
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FORMULA
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MAPLE
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a:= n-> mul(2^n-2^i, i=0..n-1)*numtheory[phi](2^n-1)/((2^n-1)*n):
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MATHEMATICA
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nn = 13; Table[EulerPhi[2^n - 1]/n, {n, 1, nn}]* Table[Product[2^n - 2^i, {i, 0, n - 1}], {n, 1, nn}]/Table[2^n - 1, {n, 1, nn}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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