A309469 Sum of the prime parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 7, 11, 28, 41, 79, 115, 191, 255, 389, 517, 752, 976, 1335, 1707, 2289, 2870, 3737, 4639, 5904, 7246, 9088, 11040, 13635, 16416, 19984, 23856, 28776, 34054, 40667, 47796, 56553, 66043, 77527, 89992, 104963, 121151, 140303

Offset

0,10

Links

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

Index entries for sequences related to partitions

Formula

a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} (i * c(i) + j * c(j) + k * c(k) + l * c(l) + m * c(m) + o * c(o) + p * c(p) + (n-i-j-k-l-m-o-p) * c(n-i-j-k-l-m-o-p)), where c is the prime characteristic (A010051).

Mathematica

Table[Sum[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]) + p (PrimePi[p] - PrimePi[p - 1]) + (n - i - j - k - l - m - o - p) (PrimePi[n - i - j - k - l - m - o - p] - PrimePi[n - i - j - k - l - m - o - p - 1]), {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]

Crossrefs

Cf. A010051, A309437, A309465, A309466, A309467, A309468, A309469, A309470, A309471.

Sequence in context: A309466 A309467 A309468 * A309470 A309471 A073602

Adjacent sequences: A309466 A309467 A309468 * A309470 A309471 A309472

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 03 2019

Status

approved