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 A309427 #11 Sep 10 2019 21:41:16
%S A309427 0,0,0,0,0,0,1,3,5,11,17,24,32,46,57,77,92,118,141,175,204,249,287,
%T A309427 342,390,459,517,600,672,771,859,975,1078,1214,1336,1495,1636,1818,
%U A309427 1982,2190,2378,2615,2830,3097,3340,3641,3915,4250,4557,4930,5273,5687,6068
%N A309427 Number of prime parts in the partitions of n into 5 parts.
%H A309427 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A309427 a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-1)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} (A010051(i) + A010051(j) + A010051(k) + A010051(l) + A010051(n-i-j-k-l)).
%e A309427 Figure 1: The partitions of n into 5 parts for n = 10, 11, ..
%e A309427 1+1+1+1+10
%e A309427 1+1+1+2+9
%e A309427 1+1+1+3+8
%e A309427 1+1+1+4+7
%e A309427 1+1+1+5+6
%e A309427 1+1+1+1+9 1+1+2+2+8
%e A309427 1+1+1+2+8 1+1+2+3+7
%e A309427 1+1+1+3+7 1+1+2+4+6
%e A309427 1+1+1+4+6 1+1+2+5+5
%e A309427 1+1+1+5+5 1+1+3+3+6
%e A309427 1+1+1+1+8 1+1+2+2+7 1+1+3+4+5
%e A309427 1+1+1+2+7 1+1+2+3+6 1+1+4+4+4
%e A309427 1+1+1+3+6 1+1+2+4+5 1+2+2+2+7
%e A309427 1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6
%e A309427 1+1+1+2+6 1+1+2+2+6 1+1+3+4+4 1+2+2+4+5
%e A309427 1+1+1+3+5 1+1+2+3+5 1+2+2+2+6 1+2+3+3+5
%e A309427 1+1+1+1+6 1+1+1+4+4 1+1+2+4+4 1+2+2+3+5 1+2+3+4+4
%e A309427 1+1+1+2+5 1+1+2+2+5 1+1+3+3+4 1+2+2+4+4 1+3+3+3+4
%e A309427 1+1+1+3+4 1+1+2+3+4 1+2+2+2+5 1+2+3+3+4 2+2+2+2+6
%e A309427 1+1+2+2+4 1+1+3+3+3 1+2+2+3+4 1+3+3+3+3 2+2+2+3+5
%e A309427 1+1+2+3+3 1+2+2+2+4 1+2+3+3+3 2+2+2+2+5 2+2+2+4+4
%e A309427 1+2+2+2+3 1+2+2+3+3 2+2+2+2+4 2+2+2+3+4 2+2+3+3+4
%e A309427 2+2+2+2+2 2+2+2+2+3 2+2+2+3+3 2+2+3+3+3 2+3+3+3+3
%e A309427 --------------------------------------------------------------------------
%e A309427 n | 10 11 12 13 14 ...
%e A309427 --------------------------------------------------------------------------
%e A309427 a(n) | 17 24 32 46 57 ...
%e A309427 --------------------------------------------------------------------------
%e A309427 - _Wesley Ivan Hurt_, Sep 08 2019
%t A309427 Table[Sum[Sum[Sum[Sum[(PrimePi[i] - PrimePi[i - 1]) + (PrimePi[j] - PrimePi[j - 1]) + (PrimePi[k] - PrimePi[k - 1]) + (PrimePi[l] - PrimePi[l - 1]) + (PrimePi[n - i - j - k - l] - PrimePi[n - i - j - k - l - 1]), {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 50}]
%Y A309427 Cf. A010051, A026811.
%K A309427 nonn
%O A309427 0,8
%A A309427 _Wesley Ivan Hurt_, Aug 01 2019