Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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