

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
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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

JeanFrançois Alcover, Table of n, a(n) for n = 1..1000
M. Benito, W. Creyaufmüller, J. L. Varona, and P. Zimmermann, Aliquot Sequence 3630 Ends After Reaching 100 Digits, Experimental Mathematics (2002), Volume 11, issue 2.
Eric Weisstein's World of Mathematics, Aliquot Sequence


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 = 10^45; 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 *)


CROSSREFS

Cf. A063769, A115350, A131884.
Complement of A126016.
Sequence in context: A132999 A054027 * A127161 A129657 A103679 A029916
Adjacent sequences: A080904 A080905 A080906 * A080908 A080909 A080910


KEYWORD

nonn,nice


AUTHOR

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


EXTENSIONS

Edited by N. J. A. Sloane, Aug 14 2006
More terms from Franklin T. AdamsWatters, Dec 14 2006


STATUS

approved



