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A080907
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Numbers whose aliquot sequence terminates in a 1.
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14
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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
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1,2
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COMMENTS
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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).
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LINKS
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FORMULA
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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.
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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Gabriel Cunningham (gcasey(AT)mit.edu), Mar 31 2003
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EXTENSIONS
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The fact that 840 was missing from the sequence b-file was pointed out by Philip Turecek, Sep 10 2015
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STATUS
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approved
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