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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.
3
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
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.
Sequence in context: A217327 A069404 A198689 * A172743 A015564 A070997
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 05 2018
STATUS
approved