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Numbers n where the sum of all of its divisors <= sqrt(n) exceeds the sum of all the divisors of m <= sqrt(m) for all m<n.
3

%I #13 Aug 31 2019 04:34:37

%S 1,4,9,12,16,24,30,36,60,72,90,120,144,180,240,336,360,420,480,504,

%T 600,630,672,720,840,1080,1260,1440,1680,2160,2520,3360,3600,3780,

%U 3960,4200,4320,4620,5040,6720,7560,9240,10080,12600,13860,15120,18480,20160

%N Numbers n where the sum of all of its divisors <= sqrt(n) exceeds the sum of all the divisors of m <= sqrt(m) for all m<n.

%H Amiram Eldar, <a href="/A141037/b141037.txt">Table of n, a(n) for n = 1..250</a>

%e 12 qualifies because it sets a record of 1+2+3=6. (1, 2 and 3 are the divisors of 12 <= sqrt(12).)

%t lst = {}; s = -1; Do[t = Plus @@ Select[Divisors@n, # <= Sqrt@n &]; If[t > s, AppendTo[lst, n]; s = t], {n, 25199}]; lst (* _Robert G. Wilson v_, Aug 03 2008 *)

%Y Cf. A002093 (all divisors), A034090 (all divisors except n itself).

%Y Cf. A066839, A143837 (records of sums).

%K nonn

%O 1,2

%A _J. Lowell_, Jul 28 2008

%E More terms from _Robert G. Wilson v_, Aug 03 2008