login
A320093
Number of primitive (=aperiodic) 9-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, 9, 89, 809, 7369, 66329, 597769, 5380009, 48426649, 435840569, 3922624969, 35303624809, 317733161289, 2859598458169, 25736390906489, 231627518218169, 2084647707070009, 18761829363630889, 168856464660630009, 1519708181946200889, 13677373641002598169
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{j=1..n} Sum_{d|j} 9^(d-1) * mu(j/d).
a(n) = A143327(n,9).
a(n) = Sum_{j=1..n} A143325(j,9).
a(n) = A143326(n,9) / 9.
G.f.: (1/(1 - x)) * Sum_{k>=1} mu(k) * x^k / (1 - 9*x^k). - Ilya Gutkovskiy, Dec 11 2020
MAPLE
b:= n-> add(`if`(d=n, 9^(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, 9^(d-1)*moebius(j/d))); \\ Michel Marcus, Dec 11 2020
CROSSREFS
Column k=9 of A143327.
Partial sums of A320074.
Sequence in context: A133486 A224760 A198967 * A015584 A072256 A138288
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 05 2018
STATUS
approved