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 A279585 #14 Feb 16 2025 08:33:38
%S A279585 0,0,1,3,8,11,12,12,21,21,22,41,42,42,63,63,64,74,75,75,79,79,80,80,
%T A279585 80,83,83,83,84,152,153,153,153,158,158,158,159,159,163,163,164,189,
%U A279585 190,190,193,193,194,194,194,197,197,197,205,205,205,210,210,210,211,223
%N A279585 Partial sums of A279536.
%H A279585 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A279585 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A279585 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A279585 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A279585 a(n) = Sum_{h=1..n} ( Sum_{i=3..h} A010051(i) * A010051(2h-i) * ( Sum_{j=i..2h-i} mu(j)^2 ) * (Product_{k=i..h} (1-abs(A010051(k)-A010051(2h-k))))).
%p A279585 with(numtheory): t:=n->add(add( (pi(i)-pi(i-1)) * (pi(2*h-i)-pi(2*h-i-1)) * add(mobius(j)^2, j=i..2*h-i) * (product(1-abs((pi(k)-pi(k-1))-(pi(2*h-k)-pi(2*h-k-1))), k=i..h)), i=3..h), h=1..n): seq(t(n), n=1..60);
%Y A279585 Cf. A010051, A279536.
%K A279585 nonn,easy
%O A279585 1,4
%A A279585 _Wesley Ivan Hurt_, Dec 15 2016