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

1,2

Comments

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

Links

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

Formula

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

a(n) = 10^(n-1) - Sum_{d<n,d|n} a(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

Maple

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

Crossrefs

Column k=10 of A143325.

First differences of A320094.

Cf. A008683, A074650, A143324.

Sequence in context: A069000 A250603 A221579 * A101564 A242811 A070843

Adjacent sequences: A320072 A320073 A320074 * A320076 A320077 A320078

Keyword

nonn

Author

Alois P. Heinz, Oct 05 2018

Status

approved