cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A320073 Number of length n primitive (=aperiodic or period n) 8-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.

This page as a plain text file.
%I A320073 #12 Feb 27 2019 11:53:54
%S A320073 1,7,63,504,4095,32697,262143,2096640,16777152,134213625,1073741823,
%T A320073 8589901320,68719476735,549755551737,4398046506945,35184369991680,
%U A320073 281474976710655,2251799796875328,18014398509481983,144115187941637640,1152921504606584769
%N A320073 Number of length n primitive (=aperiodic or period n) 8-ary words which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
%C A320073 Dirichlet convolution of mu(n) with 8^(n-1).
%H A320073 Alois P. Heinz, <a href="/A320073/b320073.txt">Table of n, a(n) for n = 1..1108</a>
%F A320073 a(n) = Sum_{d|n} 8^(d-1) * mu(n/d).
%F A320073 a(n) = 8^(n-1) - Sum_{d<n,d|n} a(d).
%F A320073 a(n) = A143325(n,8).
%F A320073 a(n) = A074650(n,8) * n/8.
%F A320073 a(n) = A143324(n,8) / 8.
%F A320073 G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 8*x^k). - _Ilya Gutkovskiy_, Oct 25 2018
%p A320073 a:= n-> add(`if`(d=n, 8^(n-1), -a(d)), d=numtheory[divisors](n)):
%p A320073 seq(a(n), n=1..25);
%Y A320073 Column k=8 of A143325.
%Y A320073 First differences of A320092.
%Y A320073 Cf. A008683, A074650, A143324.
%K A320073 nonn
%O A320073 1,2
%A A320073 _Alois P. Heinz_, Oct 05 2018