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 A349686 #9 Nov 27 2021 05:04:20
%S A349686 1,6,24,28,30,120,140,348,496,672,1080,2480,6048,6200,6552,6786,8128,
%T A349686 30240,32760,40640,143880,238080,435708,514080,523776,524160,556920,
%U A349686 805728,1997868,2178540,4713984,23569920,33550336,37035180,38958426,45532800,91963648,142990848
%N A349686 Numbers k such that the continued fraction of the abundancy index of k contains a single distinct element.
%C A349686 All the multiply-perfect numbers (A007691) are terms of this sequence, since the continued fraction of their abundancy index contains a single element.
%C A349686 Up to 4*10^10 the continued fractions of the abundancy indices of the terms have lengths 1, 2, 3, 5 or 11. The least terms that are corresponding to these lengths are 1, 24, 30, 348 and 1997868, respectively. Are there terms with other lengths?
%e A349686 24 is a term since the continued fraction of its abundancy index sigma(24)/24 = 5/2 = 2 + 1/2 has the elements {2, 2}.
%e A349686 30 is a term since the continued fraction of its abundancy index sigma(30)/30 = 12/5 = 2 + 1/(2 + 1/2) has the elements {2, 2, 2}.
%e A349686 143880 is a term since the continued fraction of its abundancy index sigma(143880)/143880 = 360/109 = 3 + 1/(3 + 1/(3 + 1/(3 + 1/3))) has the elements {3, 3, 3}.
%t A349686 c[n_] := ContinuedFraction[DivisorSigma[1, n] / n]; q[n_] := Length[Union[c[n]]] == 1; Select[Range[10^6], q]
%o A349686 (PARI) isok(k) = #Set(contfrac(sigma(k)/k)) == 1; \\ _Michel Marcus_, Nov 25 2021
%Y A349686 Cf. A000203, A007691, A071862, A071865, A017665, A017666, A349685.
%K A349686 nonn
%O A349686 1,2
%A A349686 _Amiram Eldar_, Nov 25 2021