A127665 Numbers whose infinitary aliquot sequences end in an infinitary amicable pair.

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

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: A096924 A354710 A031413 * A097037 A035480 A181986

Adjacent sequences: A127662 A127663 A127664 * A127666 A127667 A127668

Keyword

hard,nonn

Author

Ant King, Jan 26 2007

Status

approved