A308859 Sum of the largest parts in the partitions of n into 5 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 3, 8, 8, 15, 17, 17, 19, 35, 30, 50, 54, 61, 62, 102, 79, 129, 119, 150, 151, 233, 169, 260, 207, 300, 234, 398, 263, 467, 350, 527, 425, 667, 391, 768, 518, 839, 606, 1039, 636, 1233, 774, 1294, 918, 1612, 947, 1844, 1102

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, A308856, A308857, A308858.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[(n-i-j-k-l) (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) * (n-i-j-k-l), where c = A010051.

a(n) = A308854(n) - A308855(n) - A308856(n) - A308857(n) - A308858(n).