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 A308724 #44 Aug 03 2019 21:47:03
%S A308724 0,0,0,0,2,7,11,20,22,40,39,59,61,87,89,140,137,176,178,234,236,318,
%T A308724 313,399,401,499,501,612,614,712,714,841,843,1012,1003,1178,1180,1338,
%U A308724 1340,1567,1556,1751,1753,1989,1991,2270,2272,2574,2576,2902,2904,3247
%N A308724 Sum of the prime parts in the partitions of n into 3 parts.
%H A308724 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308724 a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (i * A010051(i) + j * A010051(j) + (n-i-j) * A010051(n-i-j)).
%e A308724 Figure 1: The partitions of n into 3 parts for n = 3, 4, ...
%e A308724 1+1+8
%e A308724 1+1+7 1+2+7
%e A308724 1+2+6 1+3+6
%e A308724 1+1+6 1+3+5 1+4+5
%e A308724 1+1+5 1+2+5 1+4+4 2+2+6
%e A308724 1+1+4 1+2+4 1+3+4 2+2+5 2+3+5
%e A308724 1+1+3 1+2+3 1+3+3 2+2+4 2+3+4 2+4+4
%e A308724 1+1+1 1+1+2 1+2+2 2+2+2 2+2+3 2+3+3 3+3+3 3+3+4 ...
%e A308724 -----------------------------------------------------------------------
%e A308724 n | 3 4 5 6 7 8 9 10 ...
%e A308724 -----------------------------------------------------------------------
%e A308724 a(n) | 0 2 7 11 20 22 40 39 ...
%e A308724 -----------------------------------------------------------------------
%t A308724 Table[Sum[Sum[i (PrimePi[i] - PrimePi[i - 1]) + j (PrimePi[j] - PrimePi[j - 1]) + (n - i - j) (PrimePi[n - i - j] - PrimePi[n - i - j - 1]), {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 50}]
%Y A308724 Cf. A010051, A309405.
%K A308724 nonn
%O A308724 0,5
%A A308724 _Wesley Ivan Hurt_, Aug 03 2019