A308922 Sum of the fourth largest parts in the partitions of n into 6 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 5, 7, 10, 7, 11, 12, 16, 14, 24, 20, 32, 29, 40, 32, 55, 37, 70, 56, 81, 59, 102, 72, 128, 85, 139, 101, 182, 112, 209, 139, 233, 151, 287, 179, 336, 209, 372, 244, 458, 258, 520, 323, 585, 354, 683, 387, 792

Offset

0,13

Links

Table of n, a(n) for n=0..62.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m) * k, where c = A010051.

a(n) = A308919(n) - A308920(n) - A308921(n) - A308923(n) - A308924(n) - A308925(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[k*(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[n - i - j - k - l - m] - PrimePi[n - i - j - k - l - m - 1]), {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]

Crossrefs

Cf. A010051, A259196, A308919, A308920, A308921, A308923, A308924, A308925.

Sequence in context: A363404 A152432 A308856 * A308978 A326460 A326546

Adjacent sequences: A308919 A308920 A308921 * A308923 A308924 A308925

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 30 2019

Status

approved