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Search: id:A127665
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| A127665 |
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Numbers whose infinitary aliquot sequences end in an infinitary amicable pair. |
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+0
5
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| 102, 114, 126, 210, 246, 258, 270, 318, 330, 342, 354, 366, 378, 388, 390, 408, 426, 436, 438, 450, 474, 484, 486, 498, 510, 522, 534, 536, 546, 552, 570, 582, 594, 600, 606, 618, 630, 642, 648, 654, 666, 672, 702, 726, 738, 750, 760, 762, 774, 786, 798
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Sometimes called the infinitary 2-cycle attractor set.
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REFERENCES
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Cohen, Graeme L.; On an Integer's Infinitary Divisors, Mathematics of Computation, Vol. 54, No. 189. (Jan., 1990), pp. 395-411.
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LINKS
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Pedersen, Jan Munch, Tables of Aliquot Cycles.
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EXAMPLE
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a(5)=246 because 246 is the fifth number whose infinitary aliquot sequence ends in an infinitary amicable pair.
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MATHEMATICA
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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[ # ]]] &]
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CROSSREFS
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Cf. A126168, A007357, A127661, A127662, A127663, A127664, A127666, A127667, A126169, A126170, A126171.
Sequence in context: A046293 A096924 A031413 this_sequence A097037 A035480 A107838
Adjacent sequences: A127662 A127663 A127664 this_sequence A127666 A127667 A127668
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KEYWORD
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hard,nonn
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AUTHOR
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Ant King (mathstutoring(AT)ntlworld.com), Jan 26 2007
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