%I #12 Feb 27 2019 11:53:47

%S 1,6,48,336,2400,16752,117648,823200,5764752,40351200,282475248,

%T 1977309600,13841287200,96888892752,678223070400,4747560686400,

%U 33232930569600,232630508205648,1628413597910448,11398895145019200,79792266297494304,558545863800808752

%N Number of length n primitive (=aperiodic or period n) 7-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 7^(n-1).

%H Alois P. Heinz, <a href="/A320072/b320072.txt">Table of n, a(n) for n = 1..1184</a>

%F a(n) = Sum_{d|n} 7^(d-1) * mu(n/d).

%F a(n) = 7^(n-1) - Sum_{d<n,d|n} a(d).

%F a(n) = A143325(n,7).

%F a(n) = A074650(n,7) * n/7.

%F a(n) = A143324(n,7) / 7.

%F G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 7*x^k). - _Ilya Gutkovskiy_, Oct 25 2018

%p a:= n-> add(`if`(d=n, 7^(n-1), -a(d)), d=numtheory[divisors](n)):

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

%Y Column k=7 of A143325.

%Y First differences of A320091.

%Y Cf. A008683, A074650, A143324.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Oct 05 2018