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A181311
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Highly abundant numbers k whose largest prime factor is less than log(k).
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2
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..4292
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A002093, A181312.
Sequence in context: A072066 A342018 A055065 * A083496 A125991 A028589
Adjacent sequences: A181308 A181309 A181310 * A181312 A181313 A181314
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe, Oct 13 2010
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STATUS
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approved
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