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A326462 Sum of the second largest parts in the partitions of n into 8 primes.

%I A326462 #7 Nov 18 2021 14:58:38
%S A326462 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,3,5,6,8,14,14,19,23,31,35,46,45,
%T A326462 62,71,86,85,119,115,162,163,205,212,275,260,356,344,435,411,559,516,
%U A326462 709,640,829,786,1060,914,1272,1112,1485,1299,1795,1501,2133
%N A326462 Sum of the second largest parts in the partitions of n into 8 primes.
%H A326462 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326462 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) * i, where c = A010051.
%F A326462 a(n) = A326455(n) - A326456(n) - A326457(n) - A326458(n) - A326459(n) - A326460(n) - A326461(n) - A326463(n).
%t A326462 Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[i * (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}]
%Y A326462 Cf. A010051, A259198, A326455, A326456, A326457, A326458, A326459, A326460, A326461, A326463.
%K A326462 nonn
%O A326462 0,17
%A A326462 _Wesley Ivan Hurt_, Jul 06 2019