A308856 Sum of the fourth largest parts in the partitions of n into 5 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 5, 7, 7, 7, 8, 12, 10, 14, 18, 20, 18, 29, 21, 32, 28, 37, 38, 56, 34, 59, 47, 72, 51, 85, 55, 101, 68, 112, 81, 139, 73, 151, 105, 179, 110, 209, 113, 244, 136, 258, 161, 323, 147, 354, 187, 387, 200, 436, 204, 501

Offset: 0

Author

Wesley Ivan Hurt, Jun 28 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259195, A308854, A308855, A308857, A308858, A308859.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[k (PrimePi[l] - PrimePi[l - 1]) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[j] - PrimePi[j - 1]) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i - j - k - l] - PrimePi[n - i - j - k - l - 1]), {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 50}]

Formula

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

a(n) = A308854(n) - A308855(n) - A308857(n) - A308858(n) - A308859(n).