A218124 Number of 7-ary sequences with primitive period n.

1, 7, 42, 336, 2352, 16800, 117264, 823536, 5762400, 40353264, 282458400, 1977326736, 13841167200, 96889010400, 678222249264, 4747561492800, 33232924804800, 232630513987200, 1628413557439536, 11398895185373136, 79792266015134400, 558545864082460128

Offset: 0

Author

Alois P. Heinz, Oct 21 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400

Crossrefs

Column k=7 of A143324.

Programs

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(7^d *mobius(n/d), d=divisors(n))):
seq(a(n), n=0..30);

Formula

a(n) = Sum_{d|n} 7^d * mu(n/d) for n>0, a(0) = 1.

G.f.: 1 + 7 * Sum_{k>=1} mu(k) * x^k / (1 - 7*x^k). - Ilya Gutkovskiy, Apr 14 2021