A320091 Number of primitive (=aperiodic) 7-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, 7, 55, 391, 2791, 19543, 137191, 960391, 6725143, 47076343, 329551591, 2306861191, 16148148391, 113037041143, 791260111543, 5538820797943, 38771751367543, 271402259573191, 1899815857483639, 13298711002502839, 93090977299997143, 651636841100805895

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1184

Formula

a(n) = Sum_{j=1..n} Sum_{d|j} 7^(d-1) * mu(j/d).

a(n) = A143327(n,7).

a(n) = Sum_{j=1..n} A143325(j,7).

a(n) = A143326(n,7) / 7.

G.f.: (1/(1 - x)) * Sum_{k>=1} mu(k) * x^k / (1 - 7*x^k). - Ilya Gutkovskiy, Dec 11 2020

Maple

b:= n-> add(`if`(d=n, 7^(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, 7^(d-1)*moebius(j/d))); \\ Michel Marcus, Dec 11 2020

Crossrefs

Column k=7 of A143327.

Partial sums of A320072.

Cf. A008683, A143325, A143326.

Sequence in context: A217327 A069404 A198689 * A172743 A015564 A070997

Adjacent sequences: A320088 A320089 A320090 * A320092 A320093 A320094

Keyword

nonn

Author

Alois P. Heinz, Oct 05 2018

Status

approved