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 A225757 #20 Oct 30 2023 07:29:07
%S A225757 14,15,206,207,957,958,1334,1335,1364,1365,1634,1635,2685,2686,2974,
%T A225757 2975,4364,4365,14841,14842,18873,18874,19358,19359,20145,20146,24957,
%U A225757 24958,33998,33999,36566,36567,42818,42819,56564,56565,64665,64666,74918,74919,79826
%N A225757 Table of consecutive numbers with the same sum of divisors.
%C A225757 Are 3 consecutive terms possible? There are none less than 10^12. See A002961. - _T. D. Noe_, May 15 2013
%H A225757 Charles R Greathouse IV, <a href="/A225757/b225757.txt">Table of n, a(n) for n = 1..1000</a> (first 226 terms from T. D. Noe)
%e A225757 Sequence begins:
%e A225757 14, 15;
%e A225757 206, 207;
%e A225757 957, 958;
%e A225757 1334, 1335;
%e A225757 etc.
%t A225757 sel = Select[Range[100000], DivisorSigma[1, #] == DivisorSigma[1, # + 1] &]; Union[sel, sel + 1]
%t A225757 Flatten[SequencePosition[DivisorSigma[1,Range[80000]],{x_,x_}]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 13 2017 *)
%o A225757 (PARI) v=List();t=[1,3];for(n=3,1e6,t=[t[2],sigma(n)];if(t[1]==t[2],listput(v,n-1);listput(v,n)));vecsort(Vec(v),,8) \\ _Charles R Greathouse IV_, May 15 2013
%Y A225757 Cf. A225756 (same number of divisors), A225758 (same number and sum of divisors), A002961 (first number of each pair).
%K A225757 nonn,tabf
%O A225757 1,1
%A A225757 _Jean-François Alcover_, May 15 2013