%I
%S 1,2,3,4,6,10,12,18,20,30,42,60,84,90,120,168,210,336,420,504,630,660,
%T 840,1008,1560,1980,2340,3120,3960,4620,4680,6120,6240,7920,9240,
%U 10920,11880,12240,13860,16380,18480,19800,21840,23760,27720,32760,36960
%N Highly abundant numbers k whose largest prime factor is greater than log(k).
%C Every highly abundant number (A002093) is either in this sequence or A181311. Although it appears that dividing any term by its largest prime factor produces another highly abundant number, this conjecture fails for 2942007868800, the 527th term.
%H Amiram Eldar, <a href="/A181312/b181312.txt">Table of n, a(n) for n = 1..5708</a>
%t seq = {}; sm = 0; Do[s = DivisorSigma[1, n]; If[s > sm, sm = s; If[FactorInteger[n][[1, 1]] > Log[n], AppendTo[seq, n]]], {n, 1, 37000}]; seq (* _Amiram Eldar_, Jan 14 2022 *)
%Y Cf. A002093, A181311.
%K nonn
%O 1,2
%A _T. D. Noe_, Oct 13 2010
