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 A168010 #26 Oct 24 2023 18:07:45
%S A168010 5,15,25,39,47,67,75,95,105,129,129,163,167,191,205,229,231,269,267,
%T A168010 299,313,337,341,379,387,409,427,459,445,505,497,529,553,573,571,627,
%U A168010 625,657,661,711,687,757,743,783,805,821,831,885,875,913,929,961,961,1011
%N A168010 a(n) = Sum of all numbers of divisors of all numbers k such that n^2 <= k < (n+1)^2.
%C A168010 A straightforward approach to calculate a(n) would require computing tau (A000005) for the 2n+1 integers between n^2 and (n+1)^2. Since Sum_{i=1..n} tau(i) can be computed by summing sqrt(n) terms, we can compute a(n) via the summation of n terms of the form 2*(floor(n*(n+2)/i)-floor((n-1)*(n+1)/i)) without the need to compute tau. Similarly for the sequence A168012. - _Chai Wah Wu_, Oct 24 2023
%H A168010 Chai Wah Wu, <a href="/A168010/b168010.txt">Table of n, a(n) for n = 1..10000 (n = 1..1000 from G. C. Greubel)</a>
%e A168010 a(2) = 15 because the numbers k are 4, 5, 6, 7 and 8 (since 2^2 <= k < 3^2) and d(4) + d(5) + d(6) + d(7) + d(8) = 3 + 2 + 4 + 2 + 4 = 15, where d(n) is the number of divisors of n (see A000005).
%t A168010 Table[Total[DivisorSigma[0,Range[n^2,(n+1)^2-1]]],{n,60}] (* _Harvey P. Dale_, Aug 17 2015 *)
%o A168010 (PARI) a(n)=sum(k=n^2,(n+1)^2-1,numdiv(k)) \\ _Franklin T. Adams-Watters_, May 14 2010
%o A168010 (Python)
%o A168010 def A168010(n):
%o A168010 a, b = n*(n+2),(n-1)*(n+1)
%o A168010 return (sum(a//k-b//k for k in range(1,n))<<1)+5 # _Chai Wah Wu_, Oct 23 2023
%Y A168010 Cf. A000005, A168011, A168012, A168013.
%K A168010 nonn
%O A168010 1,1
%A A168010 _Omar E. Pol_, Nov 16 2009
%E A168010 More terms from _Franklin T. Adams-Watters_, May 14 2010