%I #9 Jun 17 2022 13:32:22

%S 0,0,0,0,0,0,0,0,2,2,2,4,5,4,7,4,8,6,10,8,18,6,18,10,21,10,28,10,38,

%T 14,34,14,47,12,51,18,55,16,68,18,81,20,73,22,105,20,110,24,113,26,

%U 136,24,161,30,147,32,187,28,200,34,204,32,237,32,262,38,246

%N Sum of the smallest 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) * k, where c = A010051.

%F a(n) = A308809(n) - A308772(n) - A308773(n) - A308774(n).

%t Table[Sum[Sum[Sum[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 Cf. A010051, A259194, A308772, A308773, A308774, A308809.

%K nonn

%O 0,9

%A _Wesley Ivan Hurt_, Jun 23 2019