A308855 Sum of the smallest parts in the partitions of n into 5 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 4, 7, 6, 7, 6, 12, 8, 14, 12, 18, 12, 27, 14, 30, 18, 33, 22, 48, 22, 53, 26, 62, 28, 71, 30, 87, 36, 92, 42, 113, 38, 127, 48, 139, 52, 159, 52, 190, 60, 190, 68, 233, 66, 264, 76, 275, 82, 308, 82, 359, 90, 370

Offset: 0

Author

Wesley Ivan Hurt, Jun 28 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259195, A308854, A308856, A308857, A308858, A308859.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[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) * l, where c = A010051.

a(n) = A308854(n) - A308856(n) - A308857(n) - A308858(n) - A308859(n).