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%I #10 Jul 24 2017 12:35:56
%S 1,2,10,14,22,38,70,134,138,170,190,210,318,426,1398,4170,6870,8454,
%T 19866,22470,36282,38370,70770,84774,98790,132990,474642,705990,961650
%N Numbers n such that transient part of the unitary aliquot sequence for n sets a new record.
%C The unitary version of A098009.
%C The record values are in A290144.
%D Richard K. Guy, "Unitary aliquot sequences", Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004. B8, pp. 97-99.
%D Richard K. Guy and Marvin C. Wunderlich, Computing Unitary Aliquot Sequences: A Preliminary Report, University of Calgary, Department of Mathematics and Statistics, 1979.
%D H. J. J. te Riele, Unitary Aliquot Sequences, MR 139/72, Mathematisch Centrum, 1972, Amsterdam.
%D H. J. J. te Riele, Further Results On Unitary Aliquot Sequences. NW 2/73, Mathematisch Centrum, 1973, Amsterdam.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnitaryAliquotSequence.html">Unitary Aliquot Sequence</a>
%e The unitary aliquot sequence of 134 is: 134, 70, 74, 40, 14, 10, 8, 1. Its length is 8 and it is longer than the unitary aliquot sequences of all the numbers below 134.
%t usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])];
%t g[n_] := If[n > 0, usigma[n] - n, 0]; f[n_] := NestWhileList[g, n, UnsameQ, All]; a = -1; seq = {}; Do[b = Length[f[n]] - 1; If[b > a, a = b; AppendTo[seq, n]], {n, 10^6}] ; seq (* after _Giovanni Resta_ at A034448 & _Robert G. Wilson v_ at A098009 *)
%Y Cf. A098008, A098009, A098010, A127652, A127653, A127654, A127655, A290144.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Jul 21 2017
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