A218126 Number of 9-ary sequences with primitive period n.

1, 9, 72, 720, 6480, 59040, 530640, 4782960, 43040160, 387419760, 3486725280, 31381059600, 282428998560, 2541865828320, 22876787671920, 205891132034880, 1853020145805120, 16677181699666560, 150094634909047920, 1350851717672992080, 12157665455570137920

Offset: 0

Author

Alois P. Heinz, Oct 21 2012

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1047 (terms 0..350 from Alois P. Heinz)

Crossrefs

Column k=9 of A143324.

Programs

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(9^d*mobius(n/d), d=divisors(n))):
seq(a(n), n=0..30);

PARI

a(n) = if (n==0, 1, sumdiv(n, d, 9^d*moebius(n/d))); \\ Michel Marcus, Apr 15 2021

Formula

a(n) = Sum_{d|n} 9^d * mu(n/d) for n>0, a(0) = 1.

G.f.: 1 + 9 * Sum_{k>=1} mu(k) * x^k / (1 - 9*x^k). - Ilya Gutkovskiy, Apr 15 2021