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URL: https://oeis.org/A320092

⇱ A320092 - OEIS

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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.
3
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
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.
Sequence in context: A390202 A038145 A198856 * A015576 A070998 A370178
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 05 2018
STATUS
approved