|
Search: id:A127661
|
|
|
| A127661 |
|
Lengths of the infinitary aliquot sequences. |
|
+0
7
|
|
| 2, 3, 3, 3, 3, 1, 3, 4, 3, 5, 3, 5, 3, 6, 4, 3, 3, 6, 3, 6, 4, 7, 3, 8, 3, 4, 4, 6, 3, 6, 3, 4, 5, 7, 4, 7, 3, 8, 4, 8, 3, 5, 3, 4, 5, 5, 3, 7, 3, 7, 5, 7, 3, 4, 4, 6, 4, 5, 3, 1, 3, 8, 4, 5, 4, 3, 3, 8, 5, 10, 3, 3, 3, 9, 4, 9, 4, 2, 3, 8, 3, 5, 3, 10, 4, 6, 6, 8, 3, 1, 5, 7, 5, 8, 4, 9, 3, 8, 5, 7
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The length of an infinitary aliquot sequence is defined to be the length of its transient part + the length of its terminal cycle
|
|
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.
|
|
EXAMPLE
|
a(4)=3 because the infinitary aliquot sequence generated by 4 is <4,1,0> and it has length 3.
|
|
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]]; Length[iTrajectory[ # ]] &/@ Range[100]
|
|
CROSSREFS
|
Cf. A126168, A127662, A127663, A127664, A127665, A127666, A127667.
Sequence in context: A165494 A110049 A097032 this_sequence A008968 A135715 A089326
Adjacent sequences: A127658 A127659 A127660 this_sequence A127662 A127663 A127664
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Ant King (mathstutoring(AT)ntlworld.com), Jan 26 2007
|
|
|
Search completed in 0.005 seconds
|
