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A320075
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Number of length n primitive (=aperiodic or period n) 10-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
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3
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1, 9, 99, 990, 9999, 99891, 999999, 9999000, 99999900, 999989991, 9999999999, 99999899010, 999999999999, 9999998999991, 99999999989901, 999999990000000, 9999999999999999, 99999999899900100, 999999999999999999, 9999999998999999010, 99999999999998999901
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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 10^(n-1).
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LINKS
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FORMULA
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a(n) = Sum_{d|n} 10^(d-1) * mu(n/d).
a(n) = 10^(n-1) - Sum_{d<n,d|n} a(d).
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MAPLE
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a:= n-> add(`if`(d=n, 10^(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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