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%I #12 Sep 17 2021 18:12:55
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16,17,18,38,40,63,88,92,120,150,182,
%T 216,280,261,360,434,512,528,714,665,936,962,1178,1170,1560,1394,1932,
%U 1849,2332,2160,2990,2632,3696,3234,4250,3927,5408,4452,6372,5445
%N Sum of all the parts in the partitions of n into 8 primes.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = n * Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} c(p) * c(o) * c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m-o-p), where c = A010051.
%F a(n) = n * A259198(n).
%F a(n) = A326456(n) + A326457(n) + A326458(n) + A326459(n) + A326460(n) + A326461(n) + A326462(n) + A326463(n).
%t a[n_] := n*Length[IntegerPartitions[n, {8}, Prime[Range[PrimePi[n]]]]]; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Jul 07 2019 *)
%Y Cf. A010051, A259198, A326456, A326457, A326458, A326459, A326460, A326461, A326462, A326463.
%K nonn
%O 0,17
%A _Wesley Ivan Hurt_, Jul 06 2019