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 A294111 #15 Feb 05 2023 15:07:35
%S A294111 0,0,1,3,2,4,2,4,6,8,4,6,8,11,6,8,10,13,16,20,24,28,20,24,28,32,22,25,
%T A294111 28,32,36,41,46,51,38,42,46,51,36,40,44,49,54,60,66,72,54,60,66,72,78,
%U A294111 84,90,97,104,111,118,125,102,109,116,124,100,107,114
%N A294111 Sum of the smaller parts of the partitions of n into two parts with larger part prime.
%H A294111 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A294111 a(n) = Sum_{i=1..floor(n/2)} i * c(n - i), where c is the prime characteristic (A010051).
%t A294111 Table[Sum[i (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[n/2]}], {n, 80}]
%t A294111 Table[Total[Select[IntegerPartitions[n,{2}],PrimeQ[#[[1]]]&][[All,2]]],{n,70}] (* _Harvey P. Dale_, Feb 05 2023 *)
%Y A294111 Cf. A010051, A294109.
%K A294111 nonn,easy
%O A294111 1,4
%A A294111 _Wesley Ivan Hurt_, Oct 22 2017