A054720 Number of 5-ary sequences with primitive period n.

1, 5, 20, 120, 600, 3120, 15480, 78120, 390000, 1953000, 9762480, 48828120, 244124400, 1220703120, 6103437480, 30517574880, 152587500000, 762939453120, 3814695297000, 19073486328120, 95367421874400, 476837158124880, 2384185742187480, 11920928955078120

Offset: 0

Author

N. J. A. Sloane, Apr 20 2000

Keywords

• nonn

Comments

Equivalently, output sequences with primitive period n from a simple cycling shift register.

References

• E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450

Crossrefs

Column k=5 of A143324.

Programs

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(mobius(d)*5^(n/d), d=divisors(n))):
seq(a(n), n=0..30);  # Alois P. Heinz, Oct 21 2012

Mathematica

a[0] = 1; a[n_] := Sum[MoebiusMu[d]*5^(n/d), {d, Divisors[n]}]; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Mar 11 2014 *)

Formula

Sum mu(d)*5^(n/d); d|n.

a(0) = 1, a(n) = n * A001692(n).

G.f.: 1 + 5 * Sum_{k>=1} mu(k) * x^k / (1 - 5*x^k). - Ilya Gutkovskiy, Apr 14 2021