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A326790
The rank of the group of functions on the units of Z/nZ generated by the functions f(u) = u*k mod n.
0
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
OFFSET
1,3
COMMENTS
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.
LINKS
P. Deligne (with an appendix by N. Koblitz and A. Ogus), Valeurs de fonctions L et périodes d'intégrales, Proceedings of Symposia in Pure Mathematics, 33 (1979), 313-346.
PROG
(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()
CROSSREFS
Sequence in context: A286610 A335603 A304117 * A232479 A162897 A364236
KEYWORD
nonn
AUTHOR
Julian Rosen, Oct 19 2019
STATUS
approved