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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. 4
1, 6, 48, 336, 2400, 16752, 117648, 823200, 5764752, 40351200, 282475248, 1977309600, 13841287200, 96888892752, 678223070400, 4747560686400, 33232930569600, 232630508205648, 1628413597910448, 11398895145019200, 79792266297494304, 558545863800808752 (list; graph; refs; listen; history; text; internal format)
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: A166152 A300582 A049316 * A024075 A052571 A324074

Adjacent sequences:  A320069 A320070 A320071 * A320073 A320074 A320075

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 05 2018

STATUS

approved

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Last modified July 28 17:15 EDT 2021. Contains 346335 sequences. (Running on oeis4.)