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 A161842 #22 Feb 05 2025 02:50:40
%S A161842 2,4,6,10,12,16,18,22,26,30,32,38,40,44,48,54,56,62,64,70,74,78,80,88,
%T A161842 92,96,100,106,108,116,118,124,128,132,136,146,148,152,156,164,166,
%U A161842 174,176,182,188,192,194,204,208,214,218,224,226,234,238,246
%N A161842 Partial sums of A161841.
%H A161842 David A. Corneth, <a href="/A161842/b161842.txt">Table of n, a(n) for n = 1..10000</a>
%H A161842 Michael Penn, <a href="https://www.youtube.com/watch?v=SEHhzkH3ZqM">This is always even??</a>, YouTube video, 2020.
%F A161842 a(n) = 2*A094820(n).
%F A161842 a(n) = Sum_{i=1..n} (1 + A008836(i))*floor(n/i). - _Enrique Pérez Herrero_, Jul 10 2012
%F A161842 a(n) ~ (log(n) + 2*gamma - 1)*n + sqrt(n), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Jul 01 2021
%t A161842 Accumulate[2*Ceiling[DivisorSigma[0, Range[100]]/2]] (* _Paolo Xausa_, Feb 05 2025 *)
%o A161842 (PARI) a(n) = sum(i=1, n, floor(n/i)) + sqrtint(n) \\ _David A. Corneth_, Dec 17 2020
%o A161842 (PARI) first(n) = {my(res = vector(n), t = 0); for(i = 1, n, t+=(numdiv(i)+issquare(i)); res[i] = t ); res } \\ _David A. Corneth_, Dec 17 2020
%Y A161842 Cf. A001620, A008836, A038548, A094820, A161841.
%K A161842 nonn,easy
%O A161842 1,1
%A A161842 _Omar E. Pol_, Jun 23 2009