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%I #8 Oct 15 2021 14:51:33
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,4,5,7,10,10,11,15,16,20,24,26,32,
%T 43,40,51,55,64,70,93,81,111,102,132,128,172,139,202,182,243,209,296,
%U 233,352,287,402,336,495,372,577,458,661,520,800,585,938,683
%N Sum of the fourth largest parts of the partitions of n into 7 primes.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F 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)} c(i) * c(j) * c(k) * c(l) * c(m) * c(o) * c(n-i-j-k-l-m-o) * k, where c = A010051.
%F a(n) = A308974(n) - A308975(n) - A308976(n) - A308977(n) - A308979(n) - A307637(n) - A308980(n).
%t Table[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[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}]
%Y Cf. A010051, A259197, A307637, A308974, A308975, A308976, A308977, A308979, A308980.
%K nonn
%O 0,15
%A _Wesley Ivan Hurt_, Jul 04 2019
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