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 A372679 #13 May 10 2024 09:25:53 %S A372679 1,1,3,2,5,3,6,4,9,5,10,6,12,6,15,8,16,9,18,10,18,10,22,12,25,12,27, %T A372679 12,28,15,30,16,30,16,30,18,36,18,36,20,40,18,42,20,45,22,46,24,42,25, %U A372679 48,24,52,27,50,24,54,28,58,30,60,30,54,32,60,30,66,32,66,30,70,36,72,36,75,36,60,36 %N A372679 a(n) = phi(15 * n)/8. %F A372679 G.f.: Sum_{k>=1} mu(15 * k) * x^k / (1 - x^k)^2, where mu() is the Moebius function (A008683). %F A372679 Multiplicative with a(p^e) = p^e if p = 3 or 5, and (p-1)*p^(e-1) otherwise. %F A372679 Sum_{k=1..n} a(k) ~ (225/(64*Pi^2)) * n^2. - _Amiram Eldar_, May 10 2024 %t A372679 a[n_] := EulerPhi[15 * n]/8; Array[a, 100] (* _Amiram Eldar_, May 10 2024 *) %o A372679 (PARI) a(n) = eulerphi(15*n)/8; %o A372679 (PARI) my(N=80, x='x+O('x^N)); Vec(sum(k=1, N, moebius(15*k)*x^k/(1-x^k)^2)) %Y A372679 Column k=15 of A372673. %Y A372679 Cf. A008683. %K A372679 nonn,mult,easy %O A372679 1,3 %A A372679 _Seiichi Manyama_, May 10 2024