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 A168013 #17 Oct 09 2024 06:49:57
%S A168013 8,56,189,491,1007,1930,3276,5314,8082,11973,16783,23355,31314,41380,
%T A168013 53566,68510,85771,106981,130973,159470,192020,229762,271873,320779,
%U A168013 375031,436311,504464,581422,664364,759025,860907,973989,1097783,1233366,1378996,1540522
%N A168013 a(n) = Sum of all divisors of all numbers < (n+1)^2.
%C A168013 Partial sums of A168012.
%H A168013 Chai Wah Wu, <a href="/A168013/b168013.txt">Table of n, a(n) for n = 1..10000</a>
%F A168013 a(n) = A024916(n^2+2*n). - _Jason Yuen_, Oct 08 2024
%e A168013 For n=2 the a(2)=56 because the numbers < (2+1)^2 are 1,2,3,4,5,6,7 and 8. Then a(2) = sigma(1)+sigma(2)+sigma(3)+sigma(4)+sigma(5)+sigma(6)+sigma(7)+sigma(8) = 1+3+4+7+6+12+8+15 = 56, where sigma(n) is the sum of divisor of n (see A000203).
%t A168013 A168012[n_]:=Sum[DivisorSigma[1,k],{k,n^2,(n+1)^2-1}];
%t A168013 Accumulate[Array[A168012,50]] (* _Paolo Xausa_, Oct 23 2023 *)
%o A168013 (Python)
%o A168013 def A168013(n):
%o A168013 m = n*(n+2)
%o A168013 return sum((q:=m//k)*((k<<1)+q+1) for k in range(1,n+1))-n**2*(n+1)>>1 # _Chai Wah Wu_, Oct 23 2023
%Y A168013 Cf. A000203, A024916, A168010, A168011, A168012.
%K A168013 nonn
%O A168013 1,1
%A A168013 _Omar E. Pol_, Nov 16 2009
%E A168013 More terms from _Sean A. Irvine_, Dec 07 2009