%I #17 Apr 15 2021 13:11:52

%S 1,9,72,720,6480,59040,530640,4782960,43040160,387419760,3486725280,

%T 31381059600,282428998560,2541865828320,22876787671920,

%U 205891132034880,1853020145805120,16677181699666560,150094634909047920,1350851717672992080,12157665455570137920

%N Number of 9-ary sequences with primitive period n.

%H Seiichi Manyama, <a href="/A218126/b218126.txt">Table of n, a(n) for n = 0..1047</a> (terms 0..350 from Alois P. Heinz)

%F a(n) = Sum_{d|n} 9^d * mu(n/d) for n>0, a(0) = 1.

%F G.f.: 1 + 9 * Sum_{k>=1} mu(k) * x^k / (1 - 9*x^k). - _Ilya Gutkovskiy_, Apr 15 2021

%p with(numtheory):

%p a:= n-> `if`(n=0, 1, add(9^d*mobius(n/d), d=divisors(n))):

%p seq(a(n), n=0..30);

%o (PARI) a(n) = if (n==0, 1, sumdiv(n, d, 9^d*moebius(n/d))); \\ _Michel Marcus_, Apr 15 2021

%Y Column k=9 of A143324.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 21 2012