A320071 Number of length n primitive (=aperiodic or period n) 6-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

1, 5, 35, 210, 1295, 7735, 46655, 279720, 1679580, 10076395, 60466175, 362789070, 2176782335, 13060647355, 78364162765, 470184704640, 2821109907455, 16926657757380, 101559956668415, 609359729932590, 3656158440016285, 21936950579911675, 131621703842267135

Offset

1,2

Comments

Dirichlet convolution of mu(n) with 6^(n-1).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1286

Formula

a(n) = Sum_{d|n} 6^(d-1) * mu(n/d).

a(n) = 6^(n-1) - Sum_{d<n,d|n} a(d).

a(n) = A143325(n,6).

a(n) = A074650(n,6) * n/6.

a(n) = A143324(n,6) / 6.

G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 6*x^k). - Ilya Gutkovskiy, Oct 25 2018

Maple

a:= n-> add(`if`(d=n, 6^(n-1), -a(d)), d=numtheory[divisors](n)):
seq(a(n), n=1..25);

Mathematica

nmax = 20; Rest[CoefficientList[Series[Sum[MoebiusMu[k] * x^k / (1 - 6*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Dec 11 2020 *)

Crossrefs

Column k=6 of A143325.

First differences of A320090.

Cf. A008683, A074650, A143324.

Sequence in context: A352404 A356391 A221578 * A024062 A180250 A002074

Adjacent sequences: A320068 A320069 A320070 * A320072 A320073 A320074

Keyword

nonn

Author

Alois P. Heinz, Oct 05 2018

Status

approved