A309467 Sum of the prime parts in the partitions of n into 6 parts.

0, 0, 0, 0, 0, 0, 0, 2, 7, 11, 28, 41, 79, 101, 160, 210, 310, 392, 559, 683, 909, 1126, 1464, 1766, 2250, 2687, 3345, 3977, 4853, 5701, 6886, 8012, 9522, 11036, 12979, 14888, 17388, 19842, 22936, 26053, 29853, 33725, 38496, 43219, 48947, 54800, 61768, 68800

Offset: 0

Author

Wesley Ivan Hurt, Aug 03 2019

Keywords

• nonn

Links

• David A. Corneth, Table of n, a(n) for n = 0..9999
• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A309433, A309465, A309466, A309467, A309468, A309469, A309470, A309471.

Programs

Mathematica

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

Formula

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