A218125 Number of 8-ary sequences with primitive period n.

1, 8, 56, 504, 4032, 32760, 261576, 2097144, 16773120, 134217216, 1073709000, 8589934584, 68719210560, 549755813880, 4398044413896, 35184372055560, 281474959933440, 2251799813685240, 18014398375002624, 144115188075855864, 1152921503533101120

Offset: 0

Author

Alois P. Heinz, Oct 21 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..350

Crossrefs

Column k=8 of A143324.

Programs

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(8^d*mobius(n/d), d=divisors(n))):
seq(a(n), n=0..30);

Formula

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

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