A320075 - OEIS

%I #12 Feb 27 2019 11:54:00

%S 1,9,99,990,9999,99891,999999,9999000,99999900,999989991,9999999999,

%T 99999899010,999999999999,9999998999991,99999999989901,

%U 999999990000000,9999999999999999,99999999899900100,999999999999999999,9999999998999999010,99999999999998999901

%N 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.

%C Dirichlet convolution of mu(n) with 10^(n-1).

%H Alois P. Heinz, <a href="/A320075/b320075.txt">Table of n, a(n) for n = 1..1001</a>

%F a(n) = Sum_{d|n} 10^(d-1) * mu(n/d).

%F a(n) = 10^(n-1) - Sum_{d<n,d|n} a(d).

%F a(n) = A143325(n,10).

%F a(n) = A074650(n,10) * n/10.

%F a(n) = A143324(n,10) / 10.

%F G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 10*x^k). - _Ilya Gutkovskiy_, Oct 25 2018

%p a:= n-> add(`if`(d=n, 10^(n-1), -a(d)), d=numtheory[divisors](n)):

%p seq(a(n), n=1..25);

%Y Column k=10 of A143325.

%Y First differences of A320094.

%Y Cf. A008683, A074650, A143324.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Oct 05 2018