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%I #30 Dec 07 2020 01:28:52
%S 1,1,3,5,10,11,21,22,33,34,55,46,78,69,92,92,136,105,171,140,186,175,
%T 253,188,290,246,315,282,406,284,465,376,470,424,564,426,666,531,660,
%U 568,820,570,903,710,852,781,1081,760,1155,890,1136,996,1378,963,1420,1140
%N a(n) is the number of distinct Horadam sequences of period n.
%H Robert Israel, <a href="/A326419/b326419.txt">Table of n, a(n) for n = 1..10000</a>
%H Ovidiu D. Bagdasar and Peter J. Larcombe, <a href="https://www.fq.math.ca/Papers1/51-4/BagdasarLarcombe.pdf">On the Number of Complex Horadam Sequences with a Fixed Period</a>, Fib. Q. 51(4), 2013, 339-347.
%F a(n) = Sum_{k1<k2, lcm(k1, k2)=n} phi(k1)*phi(k2) + phi(n)*(phi(n)-1)/2, for n>= 2. See link.
%p N:= 200: # for a(1)..a(N)
%p V:= Vector(N,n -> numtheory:-phi(n)*(numtheory:-phi(n)-1)/2):
%p for k1 from 1 to N do
%p p1:= numtheory:-phi(k1);
%p for k2 from k1+1 to N do
%p n:= ilcm(k1,k2);
%p if n <= N then V[n]:= V[n] + p1*numtheory:-phi(k2) fi;
%p od:
%p od:
%p V[1]:= 1:
%p convert(V,list); # _Robert Israel_, Dec 06 2020
%o (PARI) a(n) = if (n==1, 1, eulerphi(n)*(eulerphi(n)-1)/2 + sum(k2=1, n, sum(k1=1, k2-1, if (lcm(k1, k2)==n, eulerphi(k1)*eulerphi(k2)))));
%Y Cf. A102309.
%K nonn
%O 1,3
%A _Michel Marcus_, Sep 30 2019
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