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A308922 Sum of the fourth largest parts in the partitions of n into 6 primes.

%I A308922 #9 Oct 15 2021 15:05:06
%S A308922 0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,4,5,7,10,7,11,12,16,14,24,20,32,29,40,
%T A308922 32,55,37,70,56,81,59,102,72,128,85,139,101,182,112,209,139,233,151,
%U A308922 287,179,336,209,372,244,458,258,520,323,585,354,683,387,792
%N A308922 Sum of the fourth largest parts in the partitions of n into 6 primes.
%H A308922 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308922 a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m) * k, where c = A010051.
%F A308922 a(n) = A308919(n) - A308920(n) - A308921(n) - A308923(n) - A308924(n) - A308925(n).
%t A308922 Table[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[n - i - j - k - l - m] - PrimePi[n - i - j - k - l - m - 1]), {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]
%Y A308922 Cf. A010051, A259196, A308919, A308920, A308921, A308923, A308924, A308925.
%K A308922 nonn
%O A308922 0,13
%A A308922 _Wesley Ivan Hurt_, Jun 30 2019