A218127 Number of 10-ary sequences with primitive period n.

1, 10, 90, 990, 9900, 99990, 998910, 9999990, 99990000, 999999000, 9999899910, 99999999990, 999998990100, 9999999999990, 99999989999910, 999999999899010, 9999999900000000, 99999999999999990, 999999998999001000, 9999999999999999990, 99999999989999990100

Offset: 0

Author

Alois P. Heinz, Oct 21 2012

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000 (terms 0..300 from Alois P. Heinz)

Crossrefs

Column k=10 of A143324.

Programs

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(10^d*mobius(n/d), d=divisors(n))):
seq(a(n), n=0..30);

Formula

a(n) = Sum_{d|n} 10^d * mu(n/d) for n>0, a(0) = 1.

G.f.: 1 + 10 * Sum_{k>=1} mu(k) * x^k / (1 - 10*x^k). - Ilya Gutkovskiy, Apr 15 2021