editing

approved

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)} A010051c(i) * A010051c(j) * A010051c(k) * A010051c(l) * A010051c(m) * A010051c(o) * A010051c(n-i-j-k-l-m-o) * j, where c = A010051.

approved

editing

proposed

approved

editing

proposed

a(n) = A308974(n) - A308975(n) - A308976(n) - A308977(n) - A308978(n) - A307637(n) - A308980(n).

Cf. A010051, A259197, A307637, A308974, A308975, A308976, A308977, A308978, A308980.

allocated for Wesley Ivan HurtSum of the third 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, 2, 2, 5, 5, 8, 10, 12, 11, 19, 18, 27, 28, 35, 36, 57, 48, 67, 67, 87, 82, 121, 99, 146, 126, 176, 156, 232, 181, 271, 238, 336, 277, 414, 325, 500, 405, 588, 480, 722, 542, 843, 660, 977, 752, 1172, 851, 1374

0,15

<a href="/index/Par#part">Index entries for sequences related to partitions</a>

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)} A010051(i) * A010051(j) * A010051(k) * A010051(l) * A010051(m) * A010051(o) * A010051(n-i-j-k-l-m-o) * j.

Table[Sum[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[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}]

Cf. A010051, A259197.

allocated

nonn

Wesley Ivan Hurt, Jul 04 2019

approved

editing

allocated for Wesley Ivan Hurt

recycled

allocated

recycled

approved