A372671 - OEIS

%I #15 May 10 2024 08:49:20

%S 1,2,3,4,4,6,6,8,9,8,10,12,12,12,12,16,16,18,18,16,18,20,22,24,20,24,

%T 27,24,28,24,30,32,30,32,24,36,36,36,36,32,40,36,42,40,36,44,46,48,42,

%U 40,48,48,52,54,40,48,54,56,58,48,60,60,54,64,48,60,66,64,66,48,70,72,72,72,60

%N a(n) = phi(6 * n)/2.

%F G.f.: Sum_{k>=1} mu(6 * k) * x^k / (1 - x^k)^2, where mu() is the Moebius function (A008683).

%F Multiplicative with a(p^e) = p^e if p = 2 or 3, and (p-1)*p^(e-1) otherwise.

%o (PARI) a(n) = eulerphi(6*n)/2;

%o (PARI) my(N=80, x='x+O('x^N)); Vec(sum(k=1, N, moebius(6*k)*x^k/(1-x^k)^2))

%Y Partial sums gives A372637.

%Y Column k=6 of A372673.

%Y Cf. A008683.

%K nonn,mult,easy

%O 1,2

%A _Seiichi Manyama_, May 10 2024