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%I #10 May 29 2017 15:28:06
%S 102,114,126,210,246,258,270,318,330,342,354,366,378,388,390,408,426,
%T 436,438,450,474,484,486,498,510,522,534,536,546,552,570,582,594,600,
%U 606,618,630,642,648,654,666,672,702,726,738,750,760,762,774,786,798
%N Numbers whose infinitary aliquot sequences end in an infinitary amicable pair.
%C Sometimes called the infinitary 2-cycle attractor set.
%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)=246 because 246 is the fifth number whose infinitary aliquot sequence ends in an infinitary amicable pair.
%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]];InfinitaryAmicableNumberQ[k_]:=If[Nest[properinfinitarydivisorsum,k,2]==k && !properinfinitarydivisorsum[k]==k,True,False];Select[Range[820],InfinitaryAmicableNumberQ[Last[iTrajectory[ # ]]] &]
%Y Cf. A126168, A007357, A127661, A127662, A127663, A127664, A127666, A127667, A126169, A126170, A126171.
%K hard,nonn
%O 1,1
%A _Ant King_, Jan 26 2007
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