A320074 - OEIS

%I #12 Mar 16 2020 06:52:01

%S 1,8,80,720,6560,58960,531440,4782240,43046640,387413920,3486784400,

%T 31380999840,282429536480,2541865296880,22876792448320,

%U 205891127311680,1853020188851840,16677181656560880,150094635296999120,1350851717285570880,12157665459056397280

%N Number of length n primitive (=aperiodic or period n) 9-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

%C Dirichlet convolution of mu(n) with 9^(n-1).

%H Alois P. Heinz, <a href="/A320074/b320074.txt">Table of n, a(n) for n = 1..1048</a>

%F a(n) = Sum_{d|n} 9^(d-1) * mu(n/d).

%F a(n) = 9^(n-1) - Sum_{d<n,d|n} a(d).

%F a(n) = A143325(n,9).

%F a(n) = A074650(n,9) * n/9.

%F a(n) = A143324(n,9) / 9.

%F G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 9*x^k). - _Ilya Gutkovskiy_, Oct 25 2018

%p a:= n-> add(`if`(d=n, 9^(n-1), -a(d)), d=numtheory[divisors](n)):

%p seq(a(n), n=1..25);

%Y Column k=9 of A143325.

%Y First differences of A320093.

%Y Cf. A008683, A074650, A143324.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Oct 05 2018