A309470 Sum of the prime parts in the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 7, 11, 28, 41, 79, 115, 191, 273, 408, 553, 811, 1068, 1474, 1919, 2585, 3295, 4343, 5446, 6999, 8701, 10998, 13509, 16863, 20502, 25220, 30430, 37036, 44292, 53431, 63414, 75762, 89378, 105914, 124117, 146169, 170271, 199086

Offset

0,11

Links

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

Index entries for sequences related to partitions

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} (q * c(q) + p * c(p) + o * c(o) + m * c(m) + l * c(l) + k * c(k) + j * c(j) + i * c(i) + (n-i-j-k-l-m-o-p-q) * c(n-i-j-k-l-m-o-p-q)), where c is the prime characteristic (A010051).

Mathematica

Table[Sum[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]) + q (PrimePi[q] - PrimePi[q - 1]) + (n - i - j - k - l - m - o - p - q) (PrimePi[n - i - j - k - l - m - o - p - q] - PrimePi[n - i - j - k - l - m - o - p - q - 1]), {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

Crossrefs

Cf. A010051, A309438, A309465, A309466, A309467, A309468, A309469, A309470, A309471.

Sequence in context: A309467 A309468 A309469 * A309471 A073602 A057025

Adjacent sequences: A309467 A309468 A309469 * A309471 A309472 A309473

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 03 2019

Status

approved