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A320073
Number of length n primitive (=aperiodic or period n) 8-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
4
1, 7, 63, 504, 4095, 32697, 262143, 2096640, 16777152, 134213625, 1073741823, 8589901320, 68719476735, 549755551737, 4398046506945, 35184369991680, 281474976710655, 2251799796875328, 18014398509481983, 144115187941637640, 1152921504606584769
OFFSET
1,2
COMMENTS
Dirichlet convolution of mu(n) with 8^(n-1).
LINKS
FORMULA
a(n) = Sum_{d|n} 8^(d-1) * mu(n/d).
a(n) = 8^(n-1) - Sum_{d<n,d|n} a(d).
a(n) = A143325(n,8).
a(n) = A074650(n,8) * n/8.
a(n) = A143324(n,8) / 8.
G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 8*x^k). - Ilya Gutkovskiy, Oct 25 2018
MAPLE
a:= n-> add(`if`(d=n, 8^(n-1), -a(d)), d=numtheory[divisors](n)):
seq(a(n), n=1..25);
CROSSREFS
Column k=8 of A143325.
First differences of A320092.
Sequence in context: A123009 A219058 A182603 * A218191 A218367 A218314
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 05 2018
STATUS
approved