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

0,2

Links

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

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

Maple

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

Crossrefs

Column k=8 of A143324.

Sequence in context: A251250 A087290 A086787 * A098914 A009107 A209665

Adjacent sequences: A218122 A218123 A218124 * A218126 A218127 A218128

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2012

Status

approved