

A080907


Numbers whose aliquot sequence terminates in a 1.


13



1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

All primes are in this set because s(p) = 1 for p prime. Perfect numbers are clearly not in this set. Neither are aspiring numbers (A063769), or numbers whose aliquot sequence is a cycle (such as 220 and 284).
There are some numbers whose aliquot sequences haven't been fully determined (such as 276).


LINKS



FORMULA

n is a member if n = 1 or s(n) is a member, where s(n) is the sum of the proper factors of n.


EXAMPLE

4 is in this set because its aliquot chain is 4>3>1. 6 is not in this set because it is perfect. 25 is not in this set because its aliquot chain is 25>6.


MATHEMATICA

maxAliquot = 10^50; A131884 = {}; s[1] = 1; s[n_] := DivisorSigma[1, n]  n; selQ[n_ /; n <= 5] = True; selQ[n_] := NestWhile[s, n, If[{##}[[1]] > maxAliquot, Print["A131884: ", n]; AppendTo[A131884, n]; False, Length[{##}] < 4  {##}[[4 ;; 3]] != {##}[[2 ;; 1]]] & , All] == 1; Select[Range[1, 1100], selQ] (* JeanFrançois Alcover, Nov 14 2013, updated Sep 10 2015 *)


CROSSREFS



KEYWORD

nonn,nice


AUTHOR

Gabriel Cunningham (gcasey(AT)mit.edu), Mar 31 2003


EXTENSIONS

The fact that 840 was missing from the sequence bfile was pointed out by Philip Turecek, Sep 10 2015


STATUS

approved



