A290145 Numbers n that have a record maximum in their unitary aliquot sequence.

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

Offset

1,1

Comments

Maximum term in the aliquot sequence of n is considered only if it is larger than n.

The record values are in A290146.

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

Table of n, a(n) for n=1..14.

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;
If[b > a, a = b; AppendTo[rec, n]], {n, 10^6}] ; rec (* after Giovanni Resta at A034448 & Robert G. Wilson v at A098009 *)

Crossrefs

Cf. A098008, A098009, A098010, A290146.

Sequence in context: A044132 A044513 A209876 * A157346 A219543 A309393

Adjacent sequences: A290142 A290143 A290144 * A290146 A290147 A290148

Keyword

nonn,more

Author

Amiram Eldar, Jul 21 2017

Status

approved