cp's OEIS Frontend

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.

%I A320075 #12 Feb 27 2019 11:54:00
%S A320075 1,9,99,990,9999,99891,999999,9999000,99999900,999989991,9999999999,
%T A320075 99999899010,999999999999,9999998999991,99999999989901,
%U A320075 999999990000000,9999999999999999,99999999899900100,999999999999999999,9999999998999999010,99999999999998999901
%N 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.
%C A320075 Dirichlet convolution of mu(n) with 10^(n-1).
%H A320075 Alois P. Heinz, <a href="/A320075/b320075.txt">Table of n, a(n) for n = 1..1001</a>
%F A320075 a(n) = Sum_{d|n} 10^(d-1) * mu(n/d).
%F A320075 a(n) = 10^(n-1) - Sum_{d<n,d|n} a(d).
%F A320075 a(n) = A143325(n,10).
%F A320075 a(n) = A074650(n,10) * n/10.
%F A320075 a(n) = A143324(n,10) / 10.
%F A320075 G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 10*x^k). - _Ilya Gutkovskiy_, Oct 25 2018
%p A320075 a:= n-> add(`if`(d=n, 10^(n-1), -a(d)), d=numtheory[divisors](n)):
%p A320075 seq(a(n), n=1..25);
%Y A320075 Column k=10 of A143325.
%Y A320075 First differences of A320094.
%Y A320075 Cf. A008683, A074650, A143324.
%K A320075 nonn
%O A320075 1,2
%A A320075 _Alois P. Heinz_, Oct 05 2018