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

0,2

Links

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

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

Maple

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

Crossrefs

Column k=10 of A143324.

Sequence in context: A097394 A172199 A063945 * A322647 A243106 A046706

Adjacent sequences: A218124 A218125 A218126 * A218128 A218129 A218130

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2012

Status

approved