cp's OEIS Frontend

A320071 Number of length n primitive (=aperiodic or period n) 6-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

%I A320071 #17 Dec 11 2020 03:55:04
%S A320071 1,5,35,210,1295,7735,46655,279720,1679580,10076395,60466175,
%T A320071 362789070,2176782335,13060647355,78364162765,470184704640,
%U A320071 2821109907455,16926657757380,101559956668415,609359729932590,3656158440016285,21936950579911675,131621703842267135
%N A320071 Number of length n primitive (=aperiodic or period n) 6-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
%C A320071 Dirichlet convolution of mu(n) with 6^(n-1).
%H A320071 Alois P. Heinz, <a href="/A320071/b320071.txt">Table of n, a(n) for n = 1..1286</a>
%F A320071 a(n) = Sum_{d|n} 6^(d-1) * mu(n/d).
%F A320071 a(n) = 6^(n-1) - Sum_{d<n,d|n} a(d).
%F A320071 a(n) = A143325(n,6).
%F A320071 a(n) = A074650(n,6) * n/6.
%F A320071 a(n) = A143324(n,6) / 6.
%F A320071 G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 6*x^k). - _Ilya Gutkovskiy_, Oct 25 2018
%p A320071 a:= n-> add(`if`(d=n, 6^(n-1), -a(d)), d=numtheory[divisors](n)):
%p A320071 seq(a(n), n=1..25);
%t A320071 nmax = 20; Rest[CoefficientList[Series[Sum[MoebiusMu[k] * x^k / (1 - 6*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Dec 11 2020 *)
%Y A320071 Column k=6 of A143325.
%Y A320071 First differences of A320090.
%Y A320071 Cf. A008683, A074650, A143324.
%K A320071 nonn
%O A320071 1,2
%A A320071 _Alois P. Heinz_, Oct 05 2018