A320072 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.

1, 6, 48, 336, 2400, 16752, 117648, 823200, 5764752, 40351200, 282475248, 1977309600, 13841287200, 96888892752, 678223070400, 4747560686400, 33232930569600, 232630508205648, 1628413597910448, 11398895145019200, 79792266297494304, 558545863800808752

Offset

1,2

Comments

Dirichlet convolution of mu(n) with 7^(n-1).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1184

Formula

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

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

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

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

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

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

Maple

a:= n-> add(`if`(d=n, 7^(n-1), -a(d)), d=numtheory[divisors](n)):
seq(a(n), n=1..25);

Crossrefs

Column k=7 of A143325.

First differences of A320091.

Cf. A008683, A074650, A143324.

Sequence in context: A300582 A366658 A049316 * A024075 A052571 A324074

Adjacent sequences: A320069 A320070 A320071 * A320073 A320074 A320075

Keyword

nonn

Author

Alois P. Heinz, Oct 05 2018

Status

approved