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%I #12 May 10 2024 09:25:46
%S 1,1,2,2,4,2,6,4,6,4,10,4,13,6,8,8,16,6,18,8,12,10,22,8,20,13,18,12,
%T 28,8,30,16,20,16,24,12,36,18,26,16,40,12,42,20,24,22,46,16,42,20,32,
%U 26,52,18,40,24,36,28,58,16,60,30,36,32,52,20,66,32,44,24,70,24,72,36,40,36
%N a(n) = phi(13 * n)/12.
%F G.f.: -Sum_{k>=1} mu(13 * k) * x^k / (1 - x^k)^2, where mu() is the Moebius function (A008683).
%F Multiplicative with a(13^e) = 13^e, and a(p^e) = (p-1)*p^(e-1) if p != 13.
%F Sum_{k=1..n} a(k) ~ (169/(56*Pi^2)) * n^2. - _Amiram Eldar_, May 10 2024
%t a[n_] := EulerPhi[13 * n]/12; Array[a, 100] (* _Amiram Eldar_, May 10 2024 *)
%o (PARI) a(n) = eulerphi(13*n)/12;
%o (PARI) my(N=80, x='x+O('x^N)); Vec(-sum(k=1, N, moebius(13*k)*x^k/(1-x^k)^2))
%Y Column k=13 of A372673.
%Y Cf. A008683.
%K nonn,mult,easy
%O 1,3
%A _Seiichi Manyama_, May 10 2024
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