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A054720 Number of 5-ary sequences with primitive period n. 7
1, 5, 20, 120, 600, 3120, 15480, 78120, 390000, 1953000, 9762480, 48828120, 244124400, 1220703120, 6103437480, 30517574880, 152587500000, 762939453120, 3814695297000, 19073486328120, 95367421874400, 476837158124880, 2384185742187480, 11920928955078120 (list; graph; refs; listen; history; text; internal format)
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: A258665 A028944 A332710 * A208941 A209069 A301952

Adjacent sequences:  A054717 A054718 A054719 * A054721 A054722 A054723

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 20 2000

STATUS

approved

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Last modified November 30 17:12 EST 2021. Contains 349424 sequences. (Running on oeis4.)