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, 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

Table of n, a(n) for n=1..69.

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

Adjacent sequences: A326787 A326788 A326789 * A326791 A326792 A326793

Keyword

nonn

Author

Julian Rosen, Oct 19 2019

Status

approved