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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
Jean-François 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.
Markus Tervooren, Aliquot sequence of 840
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 = 10^50; 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] (* Jean-François Alcover, Nov 14 2013, updated Sep 10 2015 *)
CROSSREFS
Complement of A126016.
Sequence in context: A132999 A054027 A272978 * A127161 A129657 A249407
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. Adams-Watters, Dec 14 2006
The fact that 840 was missing from the sequence b-file was pointed out by Philip Turecek, Sep 10 2015
STATUS
approved

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Last modified March 1 15:29 EST 2024. Contains 370440 sequences. (Running on oeis4.)