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.
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
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Jul 21 2017
STATUS
approved