A308774 Sum of the largest parts in the partitions of n into 4 prime parts.

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, 71, 151, 113, 169, 115, 207, 102, 234, 171, 263, 168, 350, 191, 425, 220, 391, 265, 518, 246, 606, 322, 636, 383, 774, 348, 918, 477, 947, 516, 1102, 468, 1259

Offset: 0

Author

Wesley Ivan Hurt, Jun 23 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259194, A308771, A308772, A308773, A308809.

Programs

Mathematica

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}]

Formula

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.

a(n) = A308809(n) - A308771(n) - A308772(n) - A308773(n).