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 A309439 #11 May 15 2025 19:07:04
%S A309439 0,0,0,0,0,0,0,0,0,0,0,1,3,5,11,17,30,45,72,104,157,210,298,396,537,
%T A309439 698,924,1176,1521,1909,2418,2991,3729,4560,5610,6795,8254,9906,11919,
%U A309439 14180,16908,19972,23615,27706,32527,37917,44227,51267,59425,68525,79007
%N A309439 Number of prime parts in the partitions of n into 10 parts.
%H A309439 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A309439 a(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.
%t A309439 Table[Count[Flatten[IntegerPartitions[n,{10}]],_?PrimeQ],{n,0,50}] (* _Harvey P. Dale_, Dec 26 2020 *)
%Y A309439 Cf. A010051, A259201.
%K A309439 nonn
%O A309439 0,13
%A A309439 _Wesley Ivan Hurt_, Aug 03 2019