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 A152211 #29 Feb 01 2025 08:42:28
%S A152211 2,7,10,19,16,36,22,47,40,58,34,100,40,80,84,111,52,147,58,162,116,
%T A152211 124,70,252,106,146,148,224,88,312,94,255,180,190,188,415,112,212,212,
%U A152211 410,124,432,130,348,348,256,142,604
%N A152211 a(n) = n * sigma_0(n) + sigma_1(n).
%C A152211 a(n) is the sum of all parts plus the total number of parts of all partitions of n into equal parts. - _Omar E. Pol_, Nov 30 2019
%H A152211 Seiichi Manyama, <a href="/A152211/b152211.txt">Table of n, a(n) for n = 1..10000</a>
%F A152211 a(n) = n * A000005(n) + A000203(n).
%F A152211 a(n) = A038040(n) + A000203(n). - _Torlach Rush_, Feb 01 2019
%F A152211 G.f.: Sum_{k>=1} (k + 1) * x^k/(1 - x^k)^2. - _Ilya Gutkovskiy_, Aug 14 2019
%F A152211 Sum_{k=1..n} a(k) ~ (n^2/2) * (log(n) + 2*gamma + zeta(2) - 1/2), where gamma is Euler's constant (A001620). - _Amiram Eldar_, Feb 01 2025
%e A152211 For n = 4 the partitions of 4 into equal parts are [4], [2,2], [1,1,1,1]. The sum of all parts is 4 + 2 + 2 + 1 + 1 + 1 + 1 = 12. There are 7 parts, so a(4) = 12 + 7 = 19. - _Omar E. Pol_, Nov 30 2019
%t A152211 Array[Total[{#, 1} DivisorSigma[{0, 1}, #]] &, 48] (* _Michael De Vlieger_, Dec 01 2019 *)
%o A152211 (PARI) a(n) = n*numdiv(n) + sigma(n) \\ _Michel Marcus_, Jun 02 2013
%Y A152211 Cf. A000005, A000203, A038040, A094471, A244051.
%Y A152211 Cf. A001620, A013661.
%K A152211 easy,nonn
%O A152211 1,1
%A A152211 _Ctibor O. Zizka_, Nov 29 2008