login
Numbers k such that sigma(k)/k >= sigma(m)/m for all m <= k.
3

%I #27 Dec 24 2022 14:43:25

%S 1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,

%T 10080,15120,25200,27720,55440,110880,166320,277200,332640,360360,

%U 554400,665280,720720,1441440,2162160,3603600,4324320,7207200,8648640,10810800,21621600

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

%C 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

%e 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

%t 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 *)

%t DeleteDuplicates[Table[{n,DivisorSigma[1,n]/n},{n,2163*10^4}],Greater[ #1[[2]],#2[[2]]]&] [[All,1]] (* _Harvey P. Dale_, Sep 02 2022 *)

%Y Almost same as A004394.

%K nice,nonn

%O 1,2

%A _Mike Speciner_, Oct 15 2003

%E a(31)-a(40) from _Jon E. Schoenfield_, Mar 31 2018