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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

Cf. A063769, A115350, A131884.

Complement of A126016.

Sequence in context: A132999 A054027 * A127161 A129657 A249407 A103679

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. 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 February 9 18:45 EST 2016. Contains 268132 sequences.