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A326790
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The rank of the group of functions on the units of Z/nZ generated by the functions f(u) = u*k mod n.
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0
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0, 1, 2, 2, 3, 2, 4, 3, 4, 3, 6, 3, 7, 4, 5, 5, 9, 4, 10, 5, 7, 6, 12, 5, 11, 7, 10, 7, 15, 5, 16, 9, 11, 9, 13, 7, 19, 10, 13, 9, 21, 7, 22, 11, 13, 12, 24, 9, 22, 11, 17, 13, 27, 10, 21, 13, 19, 15, 30, 9, 31, 16, 19, 17, 25, 11, 34, 17, 23
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OFFSET
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1,3
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COMMENTS
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By a result of Koblitz and Ogus, a(n) is an upper bound on the number of values Gamma(k/n) (k a positive integer) that are multiplicatively independent over the algebraic numbers.
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LINKS
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PROG
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(SageMath)
def a(n):
M=[[u*k%n for u in range(n) if gcd(u, n)==1] for k in range(n)]
return matrix(M).rank()
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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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