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a(n) = phi(11 * n)/10.
1

%I #13 May 10 2024 09:25:42

%S 1,1,2,2,4,2,6,4,6,4,11,4,12,6,8,8,16,6,18,8,12,11,22,8,20,12,18,12,

%T 28,8,30,16,22,16,24,12,36,18,24,16,40,12,42,22,24,22,46,16,42,20,32,

%U 24,52,18,44,24,36,28,58,16,60,30,36,32,48,22,66,32,44,24,70,24,72,36,40,36

%N a(n) = phi(11 * n)/10.

%F G.f.: -Sum_{k>=1} mu(11 * k) * x^k / (1 - x^k)^2, where mu() is the Moebius function (A008683).

%F Multiplicative with a(11^e) = 11^e, and a(p^e) = (p-1)*p^(e-1) if p != 11.

%F Sum_{k=1..n} a(k) ~ (121/(40*Pi^2)) * n^2. - _Amiram Eldar_, May 10 2024

%t a[n_] := EulerPhi[11 * n]/10; Array[a, 100] (* _Amiram Eldar_, May 10 2024 *)

%o (PARI) a(n) = eulerphi(11*n)/10;

%o (PARI) my(N=80, x='x+O('x^N)); Vec(-sum(k=1, N, moebius(11*k)*x^k/(1-x^k)^2))

%Y Column k=11 of A372673.

%Y Cf. A008683.

%K nonn,mult,easy

%O 1,3

%A _Seiichi Manyama_, May 10 2024