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 A365264 #12 Aug 30 2023 20:49:23
%S A365264 2,4,4,6,4,12,4,12,6,12,4,24,4,12,12,12,4,24,4,24,12,12,4,36,6,12,12,
%T A365264 24,4,36,4,24,12,12,12,48,4,12,12,36,4,36,4,24,24,12,4,60,6,24,12,24,
%U A365264 4,36,12,36,12,12,4,120,4,12,24,24,12,36,4,24,12,36,4,120,4,12,24,24,12,36,4,60
%N A365264 a(n) is the smallest positive integer k whose number of divisors is larger than that of n.
%C A365264 The distinct values in this sequence together with 1 form A002182.
%H A365264 Michael De Vlieger, <a href="/A365264/b365264.txt">Table of n, a(n) for n = 1..10000</a>
%F A365264 a(n) = Min_{ k >= 1, sigma_0(k) > sigma_0(n) }, n>=1.
%F A365264 A002182(n+1) = a(a(...a(1))...) with n >= 0 iterations.
%t A365264 a365264[n_] := NestWhile[#+1&, 1, DivisorSigma[0, n]>=DivisorSigma[0, #]&]
%t A365264 a365264[{m_, n_}] := Map[a365264, Range[m, n]]
%t A365264 a365264[{1, 80}]
%o A365264 (PARI) a(n) = my(k=1, nd=numdiv(n)); while(numdiv(k) <= nd, k++); k; \\ _Michel Marcus_, Aug 29 2023
%Y A365264 Cf. A002182, A139770, A140635.
%K A365264 nonn
%O A365264 1,1
%A A365264 _Hartmut F. W. Hoft_, Aug 29 2023