A326790 - OEIS

%I #10 Oct 23 2019 15:53:30

%S 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,

%T 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,

%U 19,15,30,9,31,16,19,17,25,11,34,17,23

%N The rank of the group of functions on the units of Z/nZ generated by the functions f(u) = u*k mod n.

%C 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.

%H P. Deligne (with an appendix by N. Koblitz and A. Ogus), <a href="https://publications.ias.edu/node/379">Valeurs de fonctions L et périodes d'intégrales</a>, Proceedings of Symposia in Pure Mathematics, 33 (1979), 313-346.

%o (SageMath)

%o def a(n):

%o     M=[[u*k%n for u in range(n) if gcd(u,n)==1] for k in range(n)]

%o     return matrix(M).rank()

%K nonn

%O 1,3

%A _Julian Rosen_, Oct 19 2019