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 A085884 #13 Dec 26 2013 08:45:19
%S A085884 2,4,6,8,10,13,15,16,19,19,24,29,31,32,35,34,40,40,43,43,46,46,56,61,
%T A085884 63,64,67,66,72,73,75,76,79,78,88,92,94,95,98,97,103,99,106,104,109,
%U A085884 103,120,125,127,128,131,130,136,132,139,137,142,136,152,169,171,172,175
%N A085884 Let r and s be such that r + s = n; a(n) = maximum value of sigma(r) + sigma(s).
%H A085884 Charles R Greathouse IV, <a href="/A085884/b085884.txt">Table of n, a(n) for n = 2..10000</a>
%e A085884 a(8) = 6, the partitions are ( 1,7),(2,6),(3,5),(4,4) which give 9, 15,10,14 as the sum of the sigma function of both the parts.
%t A085884 a[n_] := Max[Total[DivisorSigma[1, #]]& /@ IntegerPartitions[n, {2}]]; Table[a[n], {n, 2, 100}] (* _Jean-François Alcover_, Dec 26 2013 *)
%o A085884 (PARI) a(n)=my(best=sigma(n-1)+1);for(k=2,n\2,best=max(best, sigma(k)+sigma(n-k)));best \\ _Charles R Greathouse IV_, Apr 06 2012
%Y A085884 Cf. A085883.
%K A085884 nonn
%O A085884 2,1
%A A085884 _Amarnath Murthy_, Jul 08 2003
%E A085884 More terms from _David Wasserman_, Feb 10 2005