A320092 Number of primitive (=aperiodic) 8-ary words with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

1, 8, 71, 575, 4670, 37367, 299510, 2396150, 19173302, 153386927, 1227128750, 9817030070, 78536506805, 628292058542, 5026338565487, 40210708557167, 321685685267822, 2573485482143150, 20587883991625133, 164703071933262773, 1317624576539847542

Offset

1,2

Links

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

Formula

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

a(n) = A143327(n,8).

a(n) = Sum_{j=1..n} A143325(j,8).

a(n) = A143326(n,8) / 8.

G.f.: (1/(1 - x)) * Sum_{k>=1} mu(k) * x^k / (1 - 8*x^k). - Ilya Gutkovskiy, Dec 11 2020

Maple

b:= n-> add(`if`(d=n, 8^(n-1), -b(d)), d=numtheory[divisors](n)):
a:= proc(n) option remember; b(n)+`if`(n<2, 0, a(n-1)) end:
seq(a(n), n=1..30);

Prog

(PARI) a(n) = sum(j=1, n, sumdiv(j, d, 8^(d-1)*moebius(j/d))); \\ Michel Marcus, Dec 11 2020

Crossrefs

Column k=8 of A143327.

Partial sums of A320073.

Cf. A008683, A143325, A143326.

Sequence in context: A193102 A038145 A198856 * A015576 A070998 A370178

Adjacent sequences: A320089 A320090 A320091 * A320093 A320094 A320095

Keyword

nonn

Author

Alois P. Heinz, Oct 05 2018

Status

approved