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%I #14 Dec 02 2023 19:08:15
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,14,15,16,34,36,57,80,84,88,138,144,200,
%T 208,243,280,406,360,496,512,627,646,910,792,1110,988,1326,1240,1763,
%U 1386,2064,1848,2520,2162,3102,2448,3773,3000,4284,3536,5247,3942
%N Sum of all the parts in the partitions of n into 7 primes.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = 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), c = A010051.
%F a(n) = n * A259197(n).
%F a(n) = A308975(n) + A308976(n) + A308977(n) + A308978(n) + A308979(n) + A307637(n) + A308980(n).
%t Table[Total[Flatten[Select[IntegerPartitions[n,{7}],AllTrue[#,PrimeQ]&]]],{n,0,60}] (* _Harvey P. Dale_, Nov 28 2023 *)
%Y Cf. A010051, A259197, A307637, A308975, A308976, A308977, A308978, A308979, A308980.
%K nonn
%O 0,15
%A _Wesley Ivan Hurt_, Jul 04 2019
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