%I #9 Jun 17 2022 13:35:53
%S 0,0,0,0,0,0,0,0,2,2,2,5,5,5,7,6,8,10,12,13,20,11,20,20,27,18,34,21,
%T 44,28,44,31,59,30,65,46,79,41,96,49,115,58,117,64,157,64,170,73,179,
%U 80,214,80,243,98,245,114,307,106,332,124,352,124,399,124
%N Sum of the third largest parts of the partitions of n into 4 prime parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F 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) * j, where c = A010051.
%F a(n) = A308809(n) - A308771(n) - A308773(n) - A308774(n).
%t Table[Sum[Sum[Sum[j (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 Cf. A010051, A259194, A308771, A308773, A308774, A308809.
%K nonn
%O 0,9
%A _Wesley Ivan Hurt_, Jun 23 2019
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