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 A070172 #31 Apr 04 2025 04:18:39
%S A070172 1,2,2,3,4,4,4,6,6,6,6,6,8,8,8,10,10,10,12,12,12,12,12,12,12,12,12,12,
%T A070172 16,16,16,18,18,18,18,18,18,18,18,20,20,20,24,24,24,24,24,24,24,24,24,
%U A070172 24,24,24,24,24,24,24,24,24,30,30,30,30,30,30,30,30,30,30,30,30,36,36
%N A070172 Smallest k such that sigma(k) >= n.
%C A070172 Also smallest m to partition n into distinct divisors of m; highly abundant numbers are record values: a(i) < A002093(n) for 1<=i < A085443(n), A002093(n) = a(A085443(n)). - _Reinhard Zumkeller_, Jun 30 2003
%C A070172 1 followed by A002093(k) appearing A034885(k+1)-A034885(k) times, for k >= 2. - _Amiram Eldar_, Apr 04 2025
%H A070172 Harvey P. Dale, <a href="/A070172/b070172.txt">Table of n, a(n) for n = 1..1000</a>
%H A070172 Amiram Eldar, <a href="/A070172/a070172.jpg">Plot of a(n)*log(log(n))/n for a sample of values of n <= 5.33*10^28</a>.
%F A070172 It seems that lim_{n -> oo} a(n)*log(log(n))/n = C = 0.6...
%t A070172 nn=80;With[{s=Table[{n,DivisorSigma[1,n]},{n,nn}]},Transpose[ Flatten[ Table[ Select[s,#[[2]]>=i&,1],{i,nn}],1]][[1]]] (* _Harvey P. Dale_, Dec 28 2013 *)
%t A070172 seq[lim_] := Module[{han = Cases[Import["https://oeis.org/A002093/b002093.txt", "Table"], {_, _}][[;; , 2]], hmax, sigma, d}, hmax = han[[-1]]; If[lim > hmax, Print["Error: lim is too large"]; {}, han = Select[han, # <= lim &]; sigma = DivisorSigma[1, han]; d = Join[{1}, Differences[sigma]]; Flatten[Table[han[[i]], {i, 1, Length[han]}, {d[[i]]}]]]]; seq[100] (* _Amiram Eldar_, Apr 04 2025 *)
%o A070172 (PARI) for(n=1,150,s=1; while(sigma(s)<n,s++); print1(s,","))
%Y A070172 Cf. A002093, A085443.
%K A070172 easy,nonn
%O A070172 1,2
%A A070172 _Benoit Cloitre_, May 06 2002