This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A326678 #12 Jan 31 2024 17:59:41
%S A326678 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,20,21,22,46,48,75,104,108,
%T A326678 140,203,240,279,352,363,476,560,648,740,950,936,1240,1353,1596,1677,
%U A326678 2112,2115,2714,2773,3312,3381,4350,4080,5304,5194,6372,6270,8008
%N A326678 Sum of all the parts in the partitions of n into 10 primes.
%H A326678 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326678 a(n) = n * Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} c(r) * c(q) * c(p) * c(o) * c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m-o-p-q-r), where c = A010051.
%F A326678 a(n) = n * A259201(n).
%F A326678 a(n) = A326679(n) + A326680(n) + A326681(n) + A326682(n) + A326683(n) + A326684(n) + A326685(n) + A326686(n) + A326687(n) + A326688(n).
%t A326678 Table[Total[Flatten[Select[IntegerPartitions[n,{10}],AllTrue[#,PrimeQ]&]]],{n,0,60}] (* _Harvey P. Dale_, Jan 31 2024 *)
%Y A326678 Cf. A010051, A259201, A326679, A326680, A326681, A326682, A326683, A326684, A326685, A326686, A326687, A326688.
%K A326678 nonn
%O A326678 0,21
%A A326678 _Wesley Ivan Hurt_, Jul 17 2019