A320074 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.

1, 8, 80, 720, 6560, 58960, 531440, 4782240, 43046640, 387413920, 3486784400, 31380999840, 282429536480, 2541865296880, 22876792448320, 205891127311680, 1853020188851840, 16677181656560880, 150094635296999120, 1350851717285570880, 12157665459056397280

Offset

1,2

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1048

Formula

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

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

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

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

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

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

Maple

a:= n-> add(`if`(d=n, 9^(n-1), -a(d)), d=numtheory[divisors](n)):
seq(a(n), n=1..25);

Crossrefs

Column k=9 of A143325.

First differences of A320093.

Cf. A008683, A074650, A143324.

Sequence in context: A145729 A280121 A182604 * A290874 A024101 A368920

Adjacent sequences: A320071 A320072 A320073 * A320075 A320076 A320077

Keyword

nonn

Author

Alois P. Heinz, Oct 05 2018

Status

approved