A290146 -id:A290146 - cp's OEIS frontend

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

Amiram Eldar, Jul 21 2017

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.

			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.

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

Cf. A098008, A098009, A098010, A290146.

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 *)

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

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