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 A333699 #12 Jul 26 2025 23:41:21
%S A333699 0,1,2,3,3,7,4,8,8,11,5,18,6,16,20,18,7,27,8,30,28,23,9,44,21,27,29,
%T A333699 41,10,58,11,41,41,34,45,68,12,38,48,72,13,83,14,62,76,45,15,98,39,72,
%U A333699 61,72,16,95,66,101,68,54,17,147,18,59,106,89,78,125,19,92,81,136
%N A333699 a(n) = Sum_{d|n} phi(n/d) * pi(d).
%C A333699 Möbius transform of A386596(n). Also, Dirichlet convolution of pi(n) and phi(n). - _Wesley Ivan Hurt_, Jul 26 2025
%F A333699 G.f.: Sum_{k>=1} Sum_{j>=1} phi(j) * x^(j*prime(k)) / (1 - x^j).
%F A333699 a(n) = Sum_{k=1..n} pi(gcd(n,k)).
%F A333699 a(n) = Sum_{d|n} A386596(d) * mu(n/d). - _Wesley Ivan Hurt_, Jul 26 2025
%t A333699 Table[Sum[EulerPhi[n/d] PrimePi[d], {d, Divisors[n]}], {n, 70}]
%t A333699 Table[Sum[PrimePi[GCD[n, k]], {k, n}], {n, 70}]
%o A333699 (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*primepi(d)); \\ _Michel Marcus_, Apr 03 2020
%Y A333699 Cf. A000010 (phi), A000720 (pi), A018804, A046992, A062774, A386596.
%K A333699 nonn
%O A333699 1,3
%A A333699 _Ilya Gutkovskiy_, Apr 02 2020