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 A127667 #13 Sep 16 2019 08:51:03
%S A127667 945,1743,2175,2655,2823,2865,3105,3375,3537,3585,3729,4209,4665,5775,
%T A127667 6559,6681,6969,7257,7263,7785,8457,8583,9657,10017,10047,10113,10395,
%U A127667 10599,10743,12285,13815,14055,14145,15015,15597,16065,17955,18529,18777,19305,19635
%N A127667 Odd integers that do not generate monotonically decreasing infinitary aliquot sequences.
%C A127667 Based on empirical evidence, approximately 98.9 % of the infinitary aliquot sequences generated by the odd integers are monotonically decreasing. This sequence represents the 1.1 % of odd integers that are the exceptions to this.
%H A127667 Amiram Eldar, <a href="/A127667/b127667.txt">Table of n, a(n) for n = 1..10000</a>
%H A127667 Graeme L. Cohen, <a href="http://dx.doi.org/10.1090/S0025-5718-1990-0993927-5">On an integer's infinitary divisors</a>, Math. Comp., 54 (1990), 395-411.
%H A127667 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Broken link]
%H A127667 J. O. M. Pedersen, <a href="http://web.archive.org/web/20140502102524/http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Via Internet Archive Wayback-Machine]
%H A127667 J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a> [Cached copy, pdf file only]
%e A127667 a(5)=2823 because 2823 is the fifth odd integer whose infinitary aliquot sequence is not monotonically decreasing.
%t A127667 ExponentList[n_Integer,factors_List]:={#,IntegerExponent[n,# ]}&/@factors;InfinitaryDivisors[1]:={1}; InfinitaryDivisors[n_Integer?Positive]:=Module[ { factors=First/@FactorInteger[n], d=Divisors[n] }, d[[Flatten[Position[ Transpose[ Thread[Function[{f,g}, BitOr[f,g]==g][ #,Last[ # ]]]&/@ Transpose[Last/@ExponentList[ #,factors]&/@d]],_?(And@@#&),{1}]] ]] ] Null;properinfinitarydivisorsum[k_]:=Plus@@InfinitaryDivisors[k]-k;g[n_] := If[n > 0,properinfinitarydivisorsum[n], 0];iTrajectory[n_] := Most[NestWhileList[g, n, UnsameQ, All]];u[n_]:=Table[n[[k+1]]<n[[k]],{k,1,Length[n]-1}];v[n_]:=If[ !MemberQ[u[n],False],True,False];data=iTrajectory/@Range[1,10^4,2];First/@Select[data,!v[ # ] &]
%Y A127667 Cf. A126168, A127661, A127666.
%K A127667 nonn
%O A127667 1,1
%A A127667 _Ant King_, Jan 26 2007
%E A127667 More terms from _Amiram Eldar_, Sep 16 2019