A308771 Sum of the smallest parts of the partitions of n into 4 prime parts.

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, 14, 34, 14, 47, 12, 51, 18, 55, 16, 68, 18, 81, 20, 73, 22, 105, 20, 110, 24, 113, 26, 136, 24, 161, 30, 147, 32, 187, 28, 200, 34, 204, 32, 237, 32, 262, 38, 246

Offset

0,9

Links

Table of n, a(n) for n=0..66.

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) * k, where c = A010051.

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

Mathematica

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}]

Crossrefs

Cf. A010051, A259194, A308772, A308773, A308774, A308809.

Sequence in context: A231351 A024681 A240327 * A007495 A122385 A035002

Adjacent sequences: A308768 A308769 A308770 * A308772 A308773 A308774

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 23 2019

Status

approved