A309468 Sum of the prime parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 0, 2, 7, 11, 28, 41, 79, 115, 175, 238, 357, 464, 670, 851, 1145, 1441, 1908, 2349, 3034, 3698, 4657, 5635, 7007, 8350, 10240, 12124, 14609, 17192, 20549, 23920, 28326, 32802, 38437, 44287, 51520, 58934, 68170, 77621, 89049, 100981

Offset

0,9

Links

David A. Corneth, Table of n, a(n) for n = 0..9999

Index entries for sequences related to partitions

Formula

a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} (i * c(i) + j * c(j) + k * c(k) + l * c(l) + m * c(m) + o * c(o) + (n-i-j-k-l-m-o) * c(n-i-j-k-l-m-o)), where c = A010051.

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[i (PrimePi[i] - PrimePi[i - 1]) + j (PrimePi[j] - PrimePi[j - 1]) + k (PrimePi[k] - PrimePi[k - 1]) + l (PrimePi[l] - PrimePi[l - 1]) + m (PrimePi[m] - PrimePi[m - 1]) + o (PrimePi[o] - PrimePi[o - 1]) + (n - i - j - k - l - m - o) (PrimePi[n - i - j - k - l - m - o] - PrimePi[n - i - j - k - l - m - o - 1]), {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 80}]

Crossrefs

Cf. A010051, A309436, A309465, A309466, A309467, A309468, A309469, A309470, A309471.

Sequence in context: A309465 A309466 A309467 * A309469 A309470 A309471

Adjacent sequences: A309465 A309466 A309467 * A309469 A309470 A309471

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 03 2019

Status

approved