A077006 Numbers k such that sigma(k)/k >= sigma(m)/m for all m <= k.

1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 360360, 554400, 665280, 720720, 1441440, 2162160, 3603600, 4324320, 7207200, 8648640, 10810800, 21621600

Offset: 1

Author

Mike Speciner, Oct 15 2003

Keywords

• nice
• nonn

Comments

A004394 is a subsequence. I searched to 2^150 for terms that are not in A004394 and found only a(29)=360360. Are there more near-miss superabundant numbers like 360360? - Jeppe Stig Nielsen, Dec 23 2022

Examples

			360360 is included in this sequence (but not in A004394) because its abundancy (sigma(k)/k = 48/11) is the same as that of the previous record holder (namely 332640). - _Gerard P. Michon_, May 20 2009
		

Crossrefs

Almost same as A004394.

Programs

Mathematica

abund[n_] := abund[n] = DivisorSigma[1, n]/n; ok[n_] := (r = True; m = 1; While[m <= n, If[abund[n] < abund[m], r = False; Break[]]; m++]; r); n = 1; A077006 = {}; While[n < 10^6, If[ok[n], Print[n]; AppendTo[ A077006, n]]; n++]; A077006 (* Jean-François Alcover, Dec 12 2011 *)
DeleteDuplicates[Table[{n,DivisorSigma[1,n]/n},{n,2163*10^4}],Greater[ #1[[2]],#2[[2]]]&] [[All,1]] (* Harvey P. Dale, Sep 02 2022 *)

Extensions

a(31)-a(40) from Jon E. Schoenfield, Mar 31 2018