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 A348585 #13 Apr 28 2025 13:23:53
%S A348585 1,8,27,375,459,620,1652,2871,3451,3956,8055,8636,8907,9844,10647,
%T A348585 12104,19491,20155,27089,27643,38180,41547,48364,62379,74875,79304,
%U A348585 83780,90692,115289,139460,146828,233729,291819,297987,324423,338547,365660,377540,392635,403575
%N A348585 Numbers k such that A113184(k) = A113184(k+1).
%C A348585 Equivalently, numbers k such that A002129(k) = -A002129(k+1).
%H A348585 Amiram Eldar, <a href="/A348585/b348585.txt">Table of n, a(n) for n = 1..250</a>
%e A348585 1 is a term since A113184(1) = A113184(2) = 1.
%e A348585 8 is a term since A113184(8) = A113184(9) = 13.
%t A348585 f[p_, e_] := If[p == 2, 2^(e + 1)-3, (p^(e + 1) - 1)/(p - 1)]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^5], s[#] == s[# + 1] &]
%t A348585 f[n_]:=Module[{dn=Divisors[n],odn,edn},odn=Select[dn,OddQ];edn=Select[dn,EvenQ];Abs[Total[odn]-Total[edn]]]; SequencePosition[f/@Range[404000],{x_,x_}][[;;,1]] (* _Harvey P. Dale_, Apr 28 2025 *)
%o A348585 (PARI) f(n) = -sumdiv(n, d, (-1)^d*d); \\ A002129
%o A348585 isok(k) = f(k) + f(k+1) == 0; \\ _Michel Marcus_, Oct 24 2021
%Y A348585 Cf. A002129, A113184.
%Y A348585 Similar sequences: A002961, A206368, A333261.
%K A348585 nonn
%O A348585 1,2
%A A348585 _Amiram Eldar_, Oct 24 2021