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A320075
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.
3
1, 9, 99, 990, 9999, 99891, 999999, 9999000, 99999900, 999989991, 9999999999, 99999899010, 999999999999, 9999998999991, 99999999989901, 999999990000000, 9999999999999999, 99999999899900100, 999999999999999999, 9999999998999999010, 99999999999998999901
OFFSET
1,2
COMMENTS
Dirichlet convolution of mu(n) with 10^(n-1).
LINKS
FORMULA
a(n) = Sum_{d|n} 10^(d-1) * mu(n/d).
a(n) = 10^(n-1) - Sum_{d<n,d|n} a(d).
a(n) = A143325(n,10).
a(n) = A074650(n,10) * n/10.
a(n) = A143324(n,10) / 10.
G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 10*x^k). - Ilya Gutkovskiy, Oct 25 2018
MAPLE
a:= n-> add(`if`(d=n, 10^(n-1), -a(d)), d=numtheory[divisors](n)):
seq(a(n), n=1..25);
CROSSREFS
Column k=10 of A143325.
First differences of A320094.
Sequence in context: A069000 A250603 A221579 * A101564 A242811 A070843
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 05 2018
STATUS
approved