This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372671 #19 May 18 2025 03:18:32
%S A372671 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 A372671 27,24,28,24,30,32,30,32,24,36,36,36,36,32,40,36,42,40,36,44,46,48,42,
%U A372671 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 A372671 a(n) = phi(6 * n)/2.
%C A372671 The number of integers k from 1 to n such that gcd(n,k) is a 3-smooth number (A003586). - _Amiram Eldar_, May 18 2025
%F A372671 G.f.: Sum_{k>=1} mu(6 * k) * x^k / (1 - x^k)^2, where mu() is the Moebius function (A008683).
%F A372671 Multiplicative with a(p^e) = p^e if p = 2 or 3, and (p-1)*p^(e-1) otherwise.
%t A372671 a[n_] := EulerPhi[6*n]/2; Array[a, 100] (* _Amiram Eldar_, May 18 2025 *)
%o A372671 (PARI) a(n) = eulerphi(6*n)/2;
%o A372671 (PARI) my(N=80, x='x+O('x^N)); Vec(sum(k=1, N, moebius(6*k)*x^k/(1-x^k)^2))
%Y A372671 Partial sums gives A372637.
%Y A372671 Column k=6 of A372673.
%Y A372671 Cf. A003586, A008683.
%K A372671 nonn,mult,easy
%O A372671 1,2
%A A372671 _Seiichi Manyama_, May 10 2024