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 A053249 #32 Oct 27 2023 22:00:45
%S A053249 4,4,8,8,12,8,8,4,6,12,10,4,16,12,8,8,8,12,16,8,8,16,16,16,16,8,16,8,
%T A053249 16,4,16,16,16,12,24,12,16,8,16,16,8,16,16,12,16,16,16,16,12,12,12,16,
%U A053249 16,40,16,16,32,12,24,32,24,16,16,24,24,4,24,16,64,24,16,8,16,16,16,24,32,32,20,16
%N A053249 Number of divisors of n such that n and n+1 have the same sum of divisors.
%H A053249 Amiram Eldar, <a href="/A053249/b053249.txt">Table of n, a(n) for n = 1..10135</a> (from the b-file at A002961; terms 1..4804 from T. D. Noe)
%F A053249 a(n) = tau(A002961(n)).
%t A053249 Reap[ Do[ If[ DivisorSigma[1, n] == DivisorSigma[1, n + 1], tau = DivisorSigma[0, n]; Print[{n, tau}]; Sow[tau]], {n, 1, 4*10^6}]][[2, 1]] (* _Jean-François Alcover_, Oct 08 2012 *)
%t A053249 DivisorSigma[0,#]&/@Flatten[Position[Partition[DivisorSigma[1,Range[ 4000000]],2,1], _?(First[#] == Last[#]&),{1},Heads->False]] (* _Harvey P. Dale_, Jul 04 2014 *)
%t A053249 DivisorSigma[0,#]&/@(SequencePosition[DivisorSigma[1,Range[4000000]],{x_,x_}][[All,1]]) (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 25 2019 *)
%o A053249 (PARI) do(lim)=my(v=List(),k=1,t); for(n=2,lim, t=sigma(n); if(t==k, listput(v, numdiv(n-1))); k=t); Vec(v) \\ _Charles R Greathouse IV_, Feb 08 2017
%o A053249 (Magma) [#Divisors(n):n in [1..4000000]| SumOfDivisors(n) eq SumOfDivisors(n+1)]; // _Marius A. Burtea_, Sep 07 2019
%Y A053249 Cf. A000203, A000005, A002961, A053215, A054002, A054003.
%K A053249 nonn,nice
%O A053249 1,1
%A A053249 _Asher Auel_, Jan 11 2000
%E A053249 More terms from _Naohiro Nomoto_, Mar 16 2001