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 A349690 #12 Nov 28 2021 02:55:56
%S A349690 1,2,3,5,6,7,9,11,12,13,17,18,19,20,23,25,27,28,29,31,33,37,40,41,43,
%T A349690 47,49,53,56,59,60,61,67,71,73,77,79,80,81,83,88,89,91,97,101,103,104,
%U A349690 107,109,113,120,121,125,127,131,137,139,145,149,151,155,157,163
%N A349690 Numbers k such that the continued fraction of the abundancy index of k contains distinct elements.
%C A349690 All the primes (A000040) are terms of this sequence, since the continued fraction of the abundancy index of a prime p is {1, p}.
%C A349690 All the multiply-perfect numbers (A007691) are terms of this sequence, since the continued fraction of their abundancy index contains a single element.
%H A349690 Amiram Eldar, <a href="/A349690/b349690.txt">Table of n, a(n) for n = 1..10000</a>
%e A349690 2 is a term since the abundancy index of 2 is 3/2 = 1 + 1/2 and the elements of the continued fraction, {1, 2}, are different.
%e A349690 4 is not a term since the abundancy index of 4 is 7/4 = 1 + 1/(1 + 1/3) and the elements of the continued fraction, {1, 1, 3}, are not distinct.
%t A349690 c[n_] := ContinuedFraction[DivisorSigma[1, n]/n]; q[n_] := Length[(cn = c[n])] == Length[DeleteDuplicates[cn]]; Select[Range[200], q]
%o A349690 (PARI) isok(k) = my(v=contfrac(sigma(k)/k)); #v == #Set(v); \\ _Michel Marcus_, Nov 25 2021
%Y A349690 Cf. A007691, A349502, A349685, A349686.
%K A349690 nonn
%O A349690 1,2
%A A349690 _Amiram Eldar_, Nov 25 2021