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).

6, 8, 13, 14, 15, 16, 17, 19, 20, 22, 23, 27, 29, 32, 42, 44, 46, 50, 54, 62, 69, 90, 92, 100, 104, 108, 110, 114, 130, 136, 148, 150, 152, 156, 166, 170, 176, 182, 184, 186, 198, 200, 202, 214, 230, 232, 234, 236, 240, 242, 244, 254, 258, 266, 272, 280, 286

Offset: 1

Author

Jack Brennen, Oct 24 2000

Keywords

• nonn

Examples

			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).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
• Eric Weisstein's World of Mathematics, Restricted Divisor Function.
• Eric Weisstein's World of Mathematics, Aliquot sequence.

Crossrefs

Cf. A001065, A005114, A057709.

Programs

Mathematica

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 *)