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A320073
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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.
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4
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1, 7, 63, 504, 4095, 32697, 262143, 2096640, 16777152, 134213625, 1073741823, 8589901320, 68719476735, 549755551737, 4398046506945, 35184369991680, 281474976710655, 2251799796875328, 18014398509481983, 144115187941637640, 1152921504606584769
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OFFSET
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1,2
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COMMENTS
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Dirichlet convolution of mu(n) with 8^(n-1).
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LINKS
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FORMULA
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a(n) = Sum_{d|n} 8^(d-1) * mu(n/d).
a(n) = 8^(n-1) - Sum_{d<n,d|n} a(d).
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MAPLE
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a:= n-> add(`if`(d=n, 8^(n-1), -a(d)), d=numtheory[divisors](n)):
seq(a(n), n=1..25);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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