A320073 Number of length n primitive (=aperiodic or period n) 8-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

1, 7, 63, 504, 4095, 32697, 262143, 2096640, 16777152, 134213625, 1073741823, 8589901320, 68719476735, 549755551737, 4398046506945, 35184369991680, 281474976710655, 2251799796875328, 18014398509481983, 144115187941637640, 1152921504606584769

Offset: 1

Author

Alois P. Heinz, Oct 05 2018

Keywords

• nonn

Comments

Dirichlet convolution of mu(n) with 8^(n-1).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1108

Crossrefs

Column k=8 of A143325.

First differences of A320092.

Cf. A008683, A074650, A143324.

Programs

Maple

a:= n-> add(`if`(d=n, 8^(n-1), -a(d)), d=numtheory[divisors](n)):
seq(a(n), n=1..25);

Formula

a(n) = Sum_{d|n} 8^(d-1) * mu(n/d).

a(n) = 8^(n-1) - Sum_{d

a(n) = A143325(n,8).

a(n) = A074650(n,8) * n/8.

a(n) = A143324(n,8) / 8.

G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 8*x^k). - Ilya Gutkovskiy, Oct 25 2018

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