A308923 Sum of the third 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, 5, 5, 8, 10, 9, 11, 16, 18, 21, 28, 27, 36, 41, 48, 46, 67, 54, 82, 78, 99, 86, 126, 104, 156, 129, 181, 152, 238, 175, 277, 221, 325, 249, 405, 295, 480, 342, 542, 394, 660, 430, 752, 517, 851, 584, 1005, 643

Offset

0,13

Links

Table of n, a(n) for n=0..61.

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) * j, where c = A010051.

a(n) = A308919(n) - A308920(n) - A308921(n) - A308922(n) - A308924(n) - A308925(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[j*(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, A308922, A308924, A308925.

Sequence in context: A308512 A308857 A244480 * A308979 A326461 A326547

Adjacent sequences: A308920 A308921 A308922 * A308924 A308925 A308926

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 30 2019

Status

approved