

A290145


Numbers n that have a record maximum in their unitary aliquot sequence.


1



30, 66, 102, 138, 174, 210, 318, 1110, 1398, 6870, 19866, 89610, 291450, 705990
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OFFSET

1,1


COMMENTS

Maximum term in the aliquot sequence of n is considered only if it is larger than n.
te Riele found the unitary aliquot sequences of all numbers < 10^5, except for 89610. He terminated the calculation of the unitary aliquot sequence of 89610 at the 541st iteration, at 114601234388928504726, while the maximum, 645856907610421353834, is reached at the 569th iteration.


REFERENCES

H. J. J. te Riele, Further Results On Unitary Aliquot Sequences. NW 2/73, Mathematisch Centrum, 1973, Amsterdam.


LINKS



EXAMPLE

The unitary aliquot sequence of 174 is: 174, 186, 198, 162, 84, 76, 24, 12, 8, 1. Its maximum is 198 which larger than the maxima of all the aliquot sequences of the numbers below 174.


MATHEMATICA

usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])];
g[n_] := If[n > 0, usigma[n]  n, 0]; f[n_] := NestWhileList[g, n, UnsameQ, All]; a = 1; rec = {}; Do[b = Length[f[n]]  2;


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



