A309436 Number of prime parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 5, 11, 17, 30, 45, 64, 87, 123, 160, 217, 275, 356, 441, 559, 681, 844, 1016, 1236, 1470, 1767, 2075, 2464, 2871, 3366, 3892, 4526, 5188, 5984, 6820, 7804, 8843, 10056, 11327, 12809, 14363, 16144, 18023, 20168, 22414, 24972

Offset: 0

Author

Wesley Ivan Hurt, Aug 03 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259197.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[(PrimePi[i] - PrimePi[i - 1]) + (PrimePi[j] - PrimePi[j - 1]) + (PrimePi[k] - PrimePi[k - 1]) + (PrimePi[l] - PrimePi[l - 1]) + (PrimePi[m] - PrimePi[m - 1]) + (PrimePi[o] - PrimePi[o - 1]) + (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, 50}]

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)} (A010051(i) + A010051(j) + A010051(k) + A010051(l) + A010051(m) + A010051(o) + A010051(n-i-j-k-l-m-o)).