

A127667


Odd integers that do not generate monotonically decreasing infinitary aliquot sequences.


6



945, 1743, 2175, 2655, 2823, 2865, 3105, 3375, 3537, 3585, 3729, 4209, 4665, 5775, 6559, 6681, 6969, 7257, 7263, 7785, 8457, 8583, 9657, 10017, 10047, 10113, 10395, 10599, 10743, 12285, 13815, 14055, 14145, 15015, 15597, 16065, 17955, 18529, 18777, 19305, 19635
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OFFSET

1,1


COMMENTS

Based on empirical evidence, approximately 98.9 % of the infinitary aliquot sequences generated by the odd integers are monotonically decreasing. This sequence represents the 1.1 % of odd integers that are the exceptions to this.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
Graeme L. Cohen, On an integer's infinitary divisors, Math. Comp., 54 (1990), 395411.
J. O. M. Pedersen, Tables of Aliquot Cycles [Broken link]
J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive WaybackMachine]
J. O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only]


EXAMPLE

a(5)=2823 because 2823 is the fifth odd integer whose infinitary aliquot sequence is not monotonically decreasing.


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]]; u[n_]:=Table[n[[k+1]]<n[[k]], {k, 1, Length[n]1}]; v[n_]:=If[ !MemberQ[u[n], False], True, False]; data=iTrajectory/@Range[1, 10^4, 2]; First/@Select[data, !v[ # ] &]


CROSSREFS

Cf. A126168, A127661, A127666.
Sequence in context: A188439 A275472 A275066 * A252184 A188263 A188342
Adjacent sequences: A127664 A127665 A127666 * A127668 A127669 A127670


KEYWORD

nonn


AUTHOR

Ant King, Jan 26 2007


EXTENSIONS

More terms from Amiram Eldar, Sep 16 2019


STATUS

approved



