A320075 Number of length n primitive (=aperiodic or period n) 10-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

1, 9, 99, 990, 9999, 99891, 999999, 9999000, 99999900, 999989991, 9999999999, 99999899010, 999999999999, 9999998999991, 99999999989901, 999999990000000, 9999999999999999, 99999999899900100, 999999999999999999, 9999999998999999010, 99999999999998999901

Offset: 1

Author

Alois P. Heinz, Oct 05 2018

Keywords

• nonn

Comments

Dirichlet convolution of mu(n) with 10^(n-1).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1001

Crossrefs

Column k=10 of A143325.

First differences of A320094.

Cf. A008683, A074650, A143324.

Programs

Maple

a:= n-> add(`if`(d=n, 10^(n-1), -a(d)), d=numtheory[divisors](n)):
seq(a(n), n=1..25);

Formula

a(n) = Sum_{d|n} 10^(d-1) * mu(n/d).

a(n) = 10^(n-1) - Sum_{d

a(n) = A143325(n,10).

a(n) = A074650(n,10) * n/10.

a(n) = A143324(n,10) / 10.

G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 10*x^k). - Ilya Gutkovskiy, Oct 25 2018

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