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A326461
Sum of the third largest parts in the partitions of n into 8 primes.
8
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 5, 5, 8, 10, 12, 14, 19, 21, 27, 34, 35, 44, 57, 64, 67, 88, 87, 115, 121, 142, 146, 191, 176, 233, 232, 289, 271, 369, 336, 455, 414, 537, 500, 687, 588, 816, 722, 974, 843, 1179, 977, 1392, 1172
OFFSET
0,17
FORMULA
a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} c(p) * c(o) * c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m-o-p) * j, where c = A010051.
a(n) = A326455(n) - A326456(n) - A326457(n) - A326458(n) - A326459(n) - A326460(n) - A326462(n) - A326463(n).
MATHEMATICA
Table[Sum[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[p] - PrimePi[p - 1]) (PrimePi[n - i - j - k - l - m - o - p] - PrimePi[n - i - j - k - l - m - o - p - 1]), {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 06 2019
STATUS
approved