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 A181311 Highly abundant numbers k whose largest prime factor is less than log(k). 2
 8, 16, 24, 36, 48, 72, 96, 108, 144, 180, 216, 240, 288, 300, 360, 480, 540, 600, 720, 960, 1080, 1200, 1260, 1440, 1620, 1680, 1800, 1920, 2100, 2160, 2400, 2520, 2880, 3024, 3240, 3360, 3600, 3780, 4200, 4320, 5040, 5760, 5880, 6300, 6720, 7200, 7560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Amiram Eldar, Table of n, a(n) for n = 1..4292 MATHEMATICA 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 *) CROSSREFS Cf. A002093, A181312. Sequence in context: A072066 A342018 A055065 * A083496 A125991 A028589 Adjacent sequences:  A181308 A181309 A181310 * A181312 A181313 A181314 KEYWORD nonn AUTHOR T. D. Noe, Oct 13 2010 STATUS approved

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Last modified May 28 03:28 EDT 2022. Contains 354110 sequences. (Running on oeis4.)