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A326460 Sum of the fourth largest parts of the partitions of n into 8 primes.

%I A326460 #7 Nov 18 2021 14:55:19
%S A326460 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,4,5,7,10,10,14,15,19,20,30,26,
%T A326460 38,43,54,51,74,64,97,93,118,111,159,132,193,172,231,202,293,243,357,
%U A326460 296,407,352,517,402,600,495,706,577,851,661,1004,800,1150
%N A326460 Sum of the fourth largest parts of the partitions of n into 8 primes.
%H A326460 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326460 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) * k, where c = A010051.
%F A326460 a(n) = A326455(n) - A326456(n) - A326457(n) - A326458(n) - A326459(n) - A326461(n) - A326462(n) - A326463(n).
%t A326460 Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[k * (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 A326460 Cf. A010051, A259198, A326455, A326456, A326457, A326458, A326459, A326461, A326462, A326463.
%K A326460 nonn
%O A326460 0,17
%A A326460 _Wesley Ivan Hurt_, Jul 06 2019