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A080907 Numbers whose aliquot sequence terminates in a 1.

%I A080907 #29 Feb 16 2025 08:32:48
%S A080907 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,
%T A080907 29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
%U A080907 52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75
%N A080907 Numbers whose aliquot sequence terminates in a 1.
%C A080907 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).
%C A080907 There are some numbers whose aliquot sequences haven't been fully determined (such as 276).
%H A080907 Jean-François Alcover, <a href="/A080907/b080907.txt">Table of n, a(n) for n = 1..1000</a>
%H A080907 M. Benito, W. Creyaufmüller, J. L. Varona, and P. Zimmermann, <a href="http://www.emis.de/journals/EM/expmath/volumes/11/11.2/3630finishes1.pdf">Aliquot Sequence 3630 Ends After Reaching 100 Digits</a>, Experimental Mathematics (2002), Volume 11, issue 2.
%H A080907 Markus Tervooren, <a href="http://factordb.com/sequences.php?se=1&amp;aq=840&amp;action=all&amp;fr=0&amp;to=100">Aliquot sequence of 840</a>
%H A080907 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AliquotSequence.html">Aliquot Sequence</a>
%F A080907 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.
%e A080907 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.
%t A080907 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 *)
%Y A080907 Cf. A063769, A115350, A131884.
%Y A080907 Complement of A126016.
%K A080907 nonn,nice
%O A080907 1,2
%A A080907 Gabriel Cunningham (gcasey(AT)mit.edu), Mar 31 2003
%E A080907 Edited by _N. J. A. Sloane_, Aug 14 2006
%E A080907 More terms from _Franklin T. Adams-Watters_, Dec 14 2006
%E A080907 The fact that 840 was missing from the sequence b-file was pointed out by _Philip Turecek_, Sep 10 2015