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

Author

Alois P. Heinz, Oct 05 2018

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Column k=6 of A143325.

First differences of A320090.

Cf. A008683, A074650, A143324.

Programs

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 *)

Formula

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

a(n) = 6^(n-1) - Sum_{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

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