A308980 Sum of the largest parts in the partitions of n into 7 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 3, 8, 8, 15, 20, 20, 24, 40, 42, 62, 66, 73, 92, 132, 122, 172, 180, 211, 237, 324, 296, 394, 370, 470, 463, 645, 521, 756, 708, 916, 845, 1146, 935, 1403, 1158, 1576, 1372, 1953, 1547, 2330, 1898, 2623, 2217

Offset

0,15

Links

Table of n, a(n) for n=0..58.

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

a(n) = A308974(n) - A308975(n) - A308976(n) - A308977(n) - A308978(n) - A308979(n) - A307637(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[(n-i-j-k-l-m-o)*(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, A308976, A308977, A308978, A308979.

Sequence in context: A308774 A308859 A308925 * A326463 A326549 A326688

Adjacent sequences: A308977 A308978 A308979 * A308981 A308982 A308983

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 04 2019

Status

approved