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

0,9

Links

Table of n, a(n) for n=0..58.

Index entries for sequences related to partitions

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).

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}]

Crossrefs

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

Sequence in context: A210752 A210599 A211879 * A308859 A308925 A308980

Adjacent sequences: A308771 A308772 A308773 * A308775 A308776 A308777

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 23 2019

Status

approved