A109510 Values of n such that sigma(n)-2n (the abundance of n) is a (nonnegative) square.

6, 12, 28, 70, 88, 108, 168, 220, 348, 496, 550, 580, 726, 748, 798, 910, 918, 952, 1032, 1120, 1200, 1240, 1504, 1644, 1672, 1840, 1888, 2140, 2205, 2392, 2470, 2472, 2814, 3190, 3222, 3580, 3804, 4030, 4648, 4732, 4758, 5032, 5670, 5830

Offset: 1

Author

Eric W. Weisstein, Jun 30 2005

Keywords

• nonn

Examples

			12 is in the sequence since sigma(12) - 2*12 = 28 - 24 = 4 = 2^2 is a square.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Abundance

Crossrefs

Cf. A000203, A000290, A023196, A033880.

Cf. A000396 (perfect numbers: a subsequence).

Programs

Mathematica

Select[Range[6000], IntegerQ@Sqrt[DivisorSigma[1, #] - 2 #] &] (* Amiram Eldar, Jun 22 2019 *)

PARI

isok(n) = issquare(sigma(n) - 2*n); \\ Michel Marcus, Jun 22 2019

Extensions

Name clarified by Amiram Eldar, Jun 22 2019