A290143 Numbers n such that transient part of the unitary aliquot sequence for n sets a new record.
1, 2, 10, 14, 22, 38, 70, 134, 138, 170, 190, 210, 318, 426, 1398, 4170, 6870, 8454, 19866, 22470, 36282, 38370, 70770, 84774, 98790, 132990, 474642, 705990, 961650
Offset: 1
Examples
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.
References
- Richard K. Guy, "Unitary aliquot sequences", Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004. B8, pp. 97-99.
- Richard K. Guy and Marvin C. Wunderlich, Computing Unitary Aliquot Sequences: A Preliminary Report, University of Calgary, Department of Mathematics and Statistics, 1979.
- H. J. J. te Riele, Unitary Aliquot Sequences, MR 139/72, Mathematisch Centrum, 1972, Amsterdam.
- H. J. J. te Riele, Further Results On Unitary Aliquot Sequences. NW 2/73, Mathematisch Centrum, 1973, Amsterdam.
Links
- Eric Weisstein's World of Mathematics, Unitary Aliquot Sequence
Programs
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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; 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 *)
Comments