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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.
4
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
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.
Sequence in context: A145729 A280121 A182604 * A290874 A024101 A368920
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 05 2018
STATUS
approved