A140522 Numbers for which sigma(n) - 2n exceeds sigma(k) - 2k for all k < n.

1, 6, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 168, 180, 240, 300, 336, 360, 420, 480, 540, 600, 660, 720, 840, 1008, 1080, 1200, 1260, 1440, 1680, 2100, 2160, 2520, 3240, 3360, 3780, 3960, 4200, 4620, 4680, 5040, 6300, 6720, 7200, 7560, 8400, 9240, 10080

Offset: 1

Author

J. Lowell, Jul 02 2008

Keywords

• nonn

Examples

			72 is the smallest number > 60 with an abundance > the abundance of 60. - _Donovan Johnson_, Jan 20 2012
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A002093 (d=0) and A034090 (d=1).

Programs

Mathematica

a = {1}; m = -1; For[n = 2, n < 20000, n++, If[DivisorSigma[1, n] - 2*n > m, m = DivisorSigma[1, n] - 2*n; AppendTo[a, n]]]; a (* Stefan Steinerberger, Aug 04 2008 *)
DeleteDuplicates[Table[{n,DivisorSigma[1,n]-2n},{n,11000}],GreaterEqual[ #1[[2]],#2[[2]]]&][[;;,1]] (* Harvey P. Dale, Mar 16 2023 *)

Extensions

More terms from Stefan Steinerberger, Aug 04 2008