A127667 - OEIS

%I #13 Sep 16 2019 08:51:03

%S 945,1743,2175,2655,2823,2865,3105,3375,3537,3585,3729,4209,4665,5775,

%T 6559,6681,6969,7257,7263,7785,8457,8583,9657,10017,10047,10113,10395,

%U 10599,10743,12285,13815,14055,14145,15015,15597,16065,17955,18529,18777,19305,19635

%N Odd integers that do not generate monotonically decreasing infinitary aliquot sequences.

%C 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 Amiram Eldar, <a href="/A127667/b127667.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Broken link]

%H 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 J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a> [Cached copy, pdf file only]

%e a(5)=2823 because 2823 is the fifth odd integer whose infinitary aliquot sequence is not monotonically decreasing.

%t 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 Cf. A126168, A127661, A127666.

%K nonn

%O 1,1

%A _Ant King_, Jan 26 2007

%E More terms from _Amiram Eldar_, Sep 16 2019