A218125 - OEIS

%I #9 Apr 15 2021 13:07:31

%S 1,8,56,504,4032,32760,261576,2097144,16773120,134217216,1073709000,

%T 8589934584,68719210560,549755813880,4398044413896,35184372055560,

%U 281474959933440,2251799813685240,18014398375002624,144115188075855864,1152921503533101120

%N Number of 8-ary sequences with primitive period n.

%H Alois P. Heinz, <a href="/A218125/b218125.txt">Table of n, a(n) for n = 0..350</a>

%F a(n) = Sum_{d|n} 8^d * mu(n/d) for n>0, a(0) = 1.

%F G.f.: 1 + 8 * Sum_{k>=1} mu(k) * x^k / (1 - 8*x^k). - _Ilya Gutkovskiy_, Apr 15 2021

%p with(numtheory):

%p a:= n-> `if`(n=0, 1, add(8^d*mobius(n/d), d=divisors(n))):

%p seq(a(n), n=0..30);

%Y Column k=8 of A143324.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 21 2012