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A127665 Numbers whose infinitary aliquot sequences end in an infinitary amicable pair. 2
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sometimes called the infinitary 2-cycle attractor set.

LINKS

Table of n, a(n) for n=1..51.

Graeme L. Cohen, On an integer's infinitary divisors, Math. Comp., 54 (1990), 395-411.

J. O. M. Pedersen, Tables of Aliquot Cycles [Broken link]

J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine]

J. O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only]

EXAMPLE

a(5)=246 because 246 is the fifth number whose infinitary aliquot sequence ends in an infinitary amicable pair.

MATHEMATICA

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[ # ]]] &]

CROSSREFS

Cf. A126168, A007357, A127661, A127662, A127663, A127664, A127666, A127667, A126169, A126170, A126171.

Sequence in context: A241179 A096924 A031413 * A097037 A035480 A181986

Adjacent sequences:  A127662 A127663 A127664 * A127666 A127667 A127668

KEYWORD

hard,nonn

AUTHOR

Ant King, Jan 26 2007

STATUS

approved

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Last modified June 4 17:09 EDT 2020. Contains 334828 sequences. (Running on oeis4.)