|
Search: id:A127664
|
|
|
| A127664 |
|
Infinitary amicable numbers. |
|
+0
5
|
|
| 114, 126, 594, 846, 1140, 1260, 4320, 5940, 7920, 8460, 8640, 10744, 10856, 11760, 12285, 13500, 14595, 17700, 25728, 35712, 43632, 44772, 45888, 49308
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
Cohen, Graeme L.; On an Integer's Infinitary Divisors, Mathematics of Computation, Vol. 54, No. 189. (1990), pp. 395-411.
|
|
LINKS
|
Pedersen, Jan Munch, Tables of Aliquot Cycles.
|
|
FORMULA
|
Non infinitary perfect numbers which satisfy A126168(A126168(n)) = n
|
|
EXAMPLE
|
a(5)=1140 because 1140 is the fifth infinitary amicable number.
|
|
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[50000], InfinitaryAmicableNumberQ[ # ] &]
|
|
CROSSREFS
|
Cf. A007357, A126168, A127661, A127662, A127663, A127665, A127666, A127667, A126169, A126170, A126171.
Sequence in context: A138693 A057440 A113537 this_sequence A063991 A065118 A095619
Adjacent sequences: A127661 A127662 A127663 this_sequence A127665 A127666 A127667
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Ant King (mathstutoring(AT)ntlworld.com), Jan 26 2007
|
|
|
Search completed in 0.002 seconds
|
