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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
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
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
Sequence in context: A342018 A369035 A055065 * A083496 A125991 A028589
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 13 2010
STATUS
approved