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A057710 Positive integers n with exactly 2 aliquot sequence predecessors. In other words, there are exactly two solutions x for which s(x)=n. The function s(x) here refers to the Restricted Divisor Function, the sum of all proper divisors of x. 4

%I

%S 6,8,13,14,15,16,17,19,20,22,23,27,29,32,42,44,46,50,54,62,69,90,92,

%T 100,104,108,110,114,130,136,148,150,152,156,166,170,176,182,184,186,

%U 198,200,202,214,230,232,234,236,240,242,244,254,258,266,272,280,286

%N Positive integers n with exactly 2 aliquot sequence predecessors. In other words, there are exactly two solutions x for which s(x)=n. The function s(x) here refers to the Restricted Divisor Function, the sum of all proper divisors of x.

%H T. D. Noe, <a href="/A057710/b057710.txt">Table of n, a(n) for n=1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RestrictedDivisorFunction.html">Restricted Divisor Function</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AliquotSequence.html">Aliquot sequence.</a>

%e 14 is a member of the sequence because s(22)=14 and s(169)=14 (and because no other integer x satisfies s(x)=14).

%t len = max = 57; f[_List] := (s = Select[ Split[ Sort[ Table[ DivisorSigma[1, n] - n, {n, 1, max *= 2}]]], Length[#] == 2 & ][[All, 1]]; s [[1 ;; Min[len, Length[s]]]]); FixedPoint[f, {}] (* _Jean-Fran├žois Alcover_, Oct 07 2011 *)

%Y Cf. A001065, A005114.

%K nonn

%O 1,1

%A _Jack Brennen_, Oct 24 2000

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Last modified February 26 19:41 EST 2020. Contains 332295 sequences. (Running on oeis4.)