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
Examples
a(5)=246 because 246 is the fifth number whose infinitary aliquot sequence ends in an infinitary amicable pair.
Links
- 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]
Crossrefs
Programs
-
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[ # ]]] &]
Comments