cp's OEIS Frontend

A057710 Positive integers k 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 is the sum of all proper divisors of x (A001065).

%I A057710 #22 Feb 16 2025 08:32:43
%S A057710 6,8,13,14,15,16,17,19,20,22,23,27,29,32,42,44,46,50,54,62,69,90,92,
%T A057710 100,104,108,110,114,130,136,148,150,152,156,166,170,176,182,184,186,
%U A057710 198,200,202,214,230,232,234,236,240,242,244,254,258,266,272,280,286
%N A057710 Positive integers k 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 is the sum of all proper divisors of x (A001065).
%H A057710 Amiram Eldar, <a href="/A057710/b057710.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H A057710 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RestrictedDivisorFunction.html">Restricted Divisor Function</a>.
%H A057710 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AliquotSequence.html">Aliquot sequence</a>.
%e A057710 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 A057710 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-François Alcover_, Oct 07 2011 *)
%Y A057710 Cf. A001065, A005114, A057709.
%K A057710 nonn
%O A057710 1,1
%A A057710 _Jack Brennen_, Oct 24 2000