cp's OEIS Frontend

A320072 Number of length n primitive (=aperiodic or period n) 7-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

%I A320072 #12 Feb 27 2019 11:53:47
%S A320072 1,6,48,336,2400,16752,117648,823200,5764752,40351200,282475248,
%T A320072 1977309600,13841287200,96888892752,678223070400,4747560686400,
%U A320072 33232930569600,232630508205648,1628413597910448,11398895145019200,79792266297494304,558545863800808752
%N A320072 Number of length n primitive (=aperiodic or period n) 7-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
%C A320072 Dirichlet convolution of mu(n) with 7^(n-1).
%H A320072 Alois P. Heinz, <a href="/A320072/b320072.txt">Table of n, a(n) for n = 1..1184</a>
%F A320072 a(n) = Sum_{d|n} 7^(d-1) * mu(n/d).
%F A320072 a(n) = 7^(n-1) - Sum_{d<n,d|n} a(d).
%F A320072 a(n) = A143325(n,7).
%F A320072 a(n) = A074650(n,7) * n/7.
%F A320072 a(n) = A143324(n,7) / 7.
%F A320072 G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 7*x^k). - _Ilya Gutkovskiy_, Oct 25 2018
%p A320072 a:= n-> add(`if`(d=n, 7^(n-1), -a(d)), d=numtheory[divisors](n)):
%p A320072 seq(a(n), n=1..25);
%Y A320072 Column k=7 of A143325.
%Y A320072 First differences of A320091.
%Y A320072 Cf. A008683, A074650, A143324.
%K A320072 nonn
%O A320072 1,2
%A A320072 _Alois P. Heinz_, Oct 05 2018