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

1,2

Comments

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

Links

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

Formula

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

a(n) = 8^(n-1) - Sum_{d<n,d|n} a(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

Maple

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

Crossrefs

Column k=8 of A143325.

First differences of A320092.

Cf. A008683, A074650, A143324.

Sequence in context: A123009 A219058 A182603 * A218191 A218367 A218314

Adjacent sequences: A320070 A320071 A320072 * A320074 A320075 A320076

Keyword

nonn

Author

Alois P. Heinz, Oct 05 2018

Status

approved