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 A163986 #10 Apr 30 2018 08:48:47
%S A163986 0,0,2,4,13,26,55,92,161,253,401,595,901,1288,1863,2611,3665,5016,
%T A163986 6895,9273,12501,16591,22001,28820,37753,48901,63285,81217,104049,
%U A163986 132328,168061,212041,267105,334654,418473,520836,647101,800496,988495,1216138,1493441,1827822,2233225,2720138,3307613,4010941,4855577,5863345,7069009,8502628,10211201
%N A163986 Sum of all repeated parts of all partitions of n.
%C A163986 See A163985 for more information.
%H A163986 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpa2dt.jpg">Illustration of the shell model of partitions (2D view)</a>
%H A163986 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpa3dt.jpg">Illustration of the shell model of partitions (3D view)</a>
%F A163986 a(0)=0, a(n)=A066186(n)-A163985(n), for n>0.
%e A163986 For n=4, the five partitions of 4 are {(4);(2,2);(3,1);(2,1,1);(1,1,1,1)}. Since 1 and 2 are repeated parts and 3 and 4 are not repeated parts (or isolated parts) then a(4)={(2+2)+(1)+(2+1+1)+(1+1+1+1)}=13.
%t A163986 Table[Total[Flatten[Select[Split[Sort[Flatten[IntegerPartitions[n]]]], Length[ #]>1&]]],{n,0,50}] (* _Harvey P. Dale_, Apr 30 2018 *)
%Y A163986 Cf. A000041, A066186, A163985.
%K A163986 easy,nonn
%O A163986 0,3
%A A163986 _Omar E. Pol_, Aug 14 2009
%E A163986 More terms from _Alois P. Heinz_, Jan 30 2011