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 A308774 #9 Jun 17 2022 13:38:20
%S A308774 0,0,0,0,0,0,0,0,2,3,3,8,8,12,17,12,19,23,30,38,54,31,62,59,79,73,119,
%T A308774 71,151,113,169,115,207,102,234,171,263,168,350,191,425,220,391,265,
%U A308774 518,246,606,322,636,383,774,348,918,477,947,516,1102,468,1259
%N A308774 Sum of the largest parts in the partitions of n into 4 prime parts.
%H A308774 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308774 a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} c(k) * c(j) * c(i) * c(n-i-j-k) * (n-i-j-k), where c = A010051.
%F A308774 a(n) = A308809(n) - A308771(n) - A308772(n) - A308773(n).
%t A308774 Table[Sum[Sum[Sum[(n - i - j - k) (PrimePi[k] - PrimePi[k - 1])*(PrimePi[j] - PrimePi[j - 1]) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i - j - k] - PrimePi[n - i - j - k - 1]), {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]
%Y A308774 Cf. A010051, A259194, A308771, A308772, A308773, A308809.
%K A308774 nonn
%O A308774 0,9
%A A308774 _Wesley Ivan Hurt_, Jun 23 2019