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%I #17 Apr 14 2021 22:25:24
%S 1,5,20,120,600,3120,15480,78120,390000,1953000,9762480,48828120,
%T 244124400,1220703120,6103437480,30517574880,152587500000,
%U 762939453120,3814695297000,19073486328120,95367421874400,476837158124880,2384185742187480,11920928955078120
%N Number of 5-ary sequences with primitive period n.
%C Equivalently, output sequences with primitive period n from a simple cycling shift register.
%D E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665.
%H Alois P. Heinz, <a href="/A054720/b054720.txt">Table of n, a(n) for n = 0..450</a>
%F Sum mu(d)*5^(n/d); d|n.
%F a(0) = 1, a(n) = n * A001692(n).
%F G.f.: 1 + 5 * Sum_{k>=1} mu(k) * x^k / (1 - 5*x^k). - _Ilya Gutkovskiy_, Apr 14 2021
%p with(numtheory):
%p a:= n-> `if`(n=0, 1, add(mobius(d)*5^(n/d), d=divisors(n))):
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Oct 21 2012
%t 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 *)
%Y Column k=5 of A143324.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Apr 20 2000
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