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%I #8 Oct 15 2021 15:04:00
%S 0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,4,4,7,9,7,9,12,14,14,18,18,24,27,31,30,
%T 43,33,50,48,61,53,75,62,93,71,100,87,134,92,148,113,170,127,202,139,
%U 232,159,257,190,314,190,343,233,392,264,452,275,520,308
%N Sum of the fifth largest parts in the partitions of n into 6 primes.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F 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-k-j-l-m) * l, where c = A010051.
%F a(n) = A308919(n) - A308920(n) - A308922(n) - A308923(n) - A308924(n) - A308925(n).
%t Table[Sum[Sum[Sum[Sum[Sum[l*(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 Cf. A010051, A259196, A308919, A308920, A308922, A308923, A308924, A308925.
%K nonn
%O 0,13
%A _Wesley Ivan Hurt_, Jun 30 2019
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