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A308980 Sum of the largest parts in the partitions of n into 7 primes.

%I A308980 #8 Oct 15 2021 14:55:27
%S A308980 0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,3,3,8,8,15,20,20,24,40,42,62,66,73,92,
%T A308980 132,122,172,180,211,237,324,296,394,370,470,463,645,521,756,708,916,
%U A308980 845,1146,935,1403,1158,1576,1372,1953,1547,2330,1898,2623,2217
%N A308980 Sum of the largest parts in the partitions of n into 7 primes.
%H A308980 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308980 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) * (n-i-j-k-l-m-o), where c = A010051.
%F A308980 a(n) = A308974(n) - A308975(n) - A308976(n) - A308977(n) - A308978(n) - A308979(n) - A307637(n).
%t A308980 Table[Sum[Sum[Sum[Sum[Sum[Sum[(n-i-j-k-l-m-o)*(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 A308980 Cf. A010051, A259197, A307637, A308974, A308975, A308976, A308977, A308978, A308979.
%K A308980 nonn
%O A308980 0,15
%A A308980 _Wesley Ivan Hurt_, Jul 04 2019