cp's OEIS Frontend

A320074 Number of length n primitive (=aperiodic or period n) 9-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

%I A320074 #12 Mar 16 2020 06:52:01
%S A320074 1,8,80,720,6560,58960,531440,4782240,43046640,387413920,3486784400,
%T A320074 31380999840,282429536480,2541865296880,22876792448320,
%U A320074 205891127311680,1853020188851840,16677181656560880,150094635296999120,1350851717285570880,12157665459056397280
%N A320074 Number of length n primitive (=aperiodic or period n) 9-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
%C A320074 Dirichlet convolution of mu(n) with 9^(n-1).
%H A320074 Alois P. Heinz, <a href="/A320074/b320074.txt">Table of n, a(n) for n = 1..1048</a>
%F A320074 a(n) = Sum_{d|n} 9^(d-1) * mu(n/d).
%F A320074 a(n) = 9^(n-1) - Sum_{d<n,d|n} a(d).
%F A320074 a(n) = A143325(n,9).
%F A320074 a(n) = A074650(n,9) * n/9.
%F A320074 a(n) = A143324(n,9) / 9.
%F A320074 G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 9*x^k). - _Ilya Gutkovskiy_, Oct 25 2018
%p A320074 a:= n-> add(`if`(d=n, 9^(n-1), -a(d)), d=numtheory[divisors](n)):
%p A320074 seq(a(n), n=1..25);
%Y A320074 Column k=9 of A143325.
%Y A320074 First differences of A320093.
%Y A320074 Cf. A008683, A074650, A143324.
%K A320074 nonn
%O A320074 1,2
%A A320074 _Alois P. Heinz_, Oct 05 2018