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 A309433 #21 May 16 2025 15:01:50
%S A309433 0,0,0,0,0,0,0,1,3,5,11,17,30,38,57,74,103,129,173,209,267,323,402,
%T A309433 477,583,683,820,954,1125,1295,1515,1727,1995,2264,2590,2917,3316,
%U A309433 3713,4188,4668,5229,5800,6470,7140,7918,8712,9618,10539,11590,12655,13862
%N A309433 Number of prime parts in the partitions of n into 6 parts.
%H A309433 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A309433 a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} (A010051(i) + A010051(j) + A010051(k) + A010051(l) + A010051(m) + A010051(n-i-j-k-l-m)).
%t A309433 Table[Count[Flatten[IntegerPartitions[n,{6}]],_?PrimeQ],{n,0,50}] (* _Harvey P. Dale_, Sep 03 2024 *)
%Y A309433 Cf. A010051, A259196, A309427.
%K A309433 nonn
%O A309433 0,9
%A A309433 _Wesley Ivan Hurt_, Aug 03 2019