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

0,2

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

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

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 *)

Crossrefs

Column k=5 of A143324.

Sequence in context: A028944 A332710 A352743 * A374658 A208941 A209069

Adjacent sequences: A054717 A054718 A054719 * A054721 A054722 A054723

Keyword

nonn

Author

N. J. A. Sloane, Apr 20 2000

Status

approved