A308976 Sum of the sixth largest parts of the partitions of n into 7 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 4, 6, 9, 9, 9, 13, 14, 18, 18, 20, 24, 32, 29, 37, 41, 47, 48, 65, 57, 76, 69, 88, 85, 115, 90, 129, 120, 157, 132, 187, 150, 225, 176, 247, 202, 298, 221, 339, 266, 385, 293, 453, 328, 522, 366, 565, 426

Offset

0,15

Links

Table of n, a(n) for n=0..64.

Index entries for sequences related to partitions

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)} c(i) * c(j) * c(k) * c(l) * c(m) * c(o) * c(n-i-j-k-l-m-o) * m, where c = A010051.

a(n) = A308974(n) - A308975(n) - A308977(n) - A308978(n) - A308979(n) - A307637(n) - A308980(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[m*(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}]

Crossrefs

Cf. A010051, A259197, A307637, A308974, A308975, A308977, A308978, A308979, A308980.

Sequence in context: A097196 A132325 A308920 * A326458 A326544 A326683

Adjacent sequences: A308973 A308974 A308975 * A308977 A308978 A308979

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 04 2019

Status

approved