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 A308773 #11 May 09 2025 15:49:06
%S A308773 0,0,0,0,0,0,0,0,2,2,3,5,6,5,11,8,13,12,20,17,28,15,32,26,41,24,53,33,
%T A308773 75,48,83,57,103,54,126,80,143,71,170,93,219,112,217,122,276,120,310,
%U A308773 145,320,148,376,160,446,190,443,218,532,196,587,240,613,246
%N A308773 Sum of the second largest parts in the partitions of n into 4 prime parts.
%H A308773 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308773 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) * i, where c = A010051.
%F A308773 a(n) = A308809(n) - A308771(n) - A308772(n) - A308774(n).
%t A308773 Table[Sum[Sum[Sum[i (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}]
%t A308773 Table[Total[Select[IntegerPartitions[n,{4}],AllTrue[#,PrimeQ]&][[;;,2]]],{n,0,70}] (* _Harvey P. Dale_, May 09 2025 *)
%Y A308773 Cf. A010051, A259194, A308771, A308772, A308774, A308809.
%K A308773 nonn
%O A308773 0,9
%A A308773 _Wesley Ivan Hurt_, Jun 23 2019