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%I #9 Jan 14 2022 06:21:56
%S 8,16,24,36,48,72,96,108,144,180,216,240,288,300,360,480,540,600,720,
%T 960,1080,1200,1260,1440,1620,1680,1800,1920,2100,2160,2400,2520,2880,
%U 3024,3240,3360,3600,3780,4200,4320,5040,5760,5880,6300,6720,7200,7560
%N Highly abundant numbers k whose largest prime factor is less than log(k).
%C Every highly abundant number (A002093) is either in this sequence or A181312. Although it appears that for every n there is at least one prime p such that n*p is another highly abundant number, this conjecture fails for 46846800, the 227th term.
%H Amiram Eldar, <a href="/A181311/b181311.txt">Table of n, a(n) for n = 1..4292</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, 8000}]; seq (* _Amiram Eldar_, Jan 14 2022 *)
%Y Cf. A002093, A181312.
%K nonn
%O 1,1
%A _T. D. Noe_, Oct 13 2010
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