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 A379655 #58 Jan 03 2025 21:46:37
%S A379655 3,6,7,12,13,14,30,31,38,39,56,62,90,120,126,127,132,182,194,216,255,
%T A379655 306,307,363,380,398,399,402,464,510,511,548,552,740,780,846,847,854,
%U A379655 920,930,960,961,992,1022,1023,1092,1093,1280,1407,1650,1658,1722,1723,1728
%N A379655 Numbers k such that k and k+1 are both possible values of the sum of divisors function (A000203).
%C A379655 Numbers k such that k and k+1 are both in A002191.
%H A379655 Amiram Eldar, <a href="/A379655/b379655.txt">Table of n, a(n) for n = 1..10000</a>
%H A379655 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts#Inversion_of_Multiplicative_Functions">PARI/GP Scripts for Miscellaneous Math Problems: Inversion of Multiplicative Functions</a> (invphi.gp).
%e A379655 3 is a term since 3 = sigma(2) and 3 + 1 = 4 = sigma(3).
%e A379655 6 is a term since 6 = sigma(5) and 6 + 1 = 7 = sigma(4).
%t A379655 seq[lim_] := Module[{v = Select[Union[DivisorSigma[1, Range[lim]]], # <= lim &]}, v[[Position[Differences[v], 1] // Flatten]]]; seq[2000]
%o A379655 (PARI) isA002191(n) = invsigmaNum(n) > 0; \\ using _Max Alekseyev_'s invphi.gp
%o A379655 list(lim) = my(q1 = isA002191(1), q2); for(k = 2, lim, q2 = isA002191(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);
%Y A379655 Cf. A000203, A342555, A342560.
%Y A379655 Subsequence of A002191.
%K A379655 nonn,easy
%O A379655 1,1
%A A379655 _Amiram Eldar_, Jan 03 2025