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 A181312 Highly abundant numbers k whose largest prime factor is greater than log(k). 2
 1, 2, 3, 4, 6, 10, 12, 18, 20, 30, 42, 60, 84, 90, 120, 168, 210, 336, 420, 504, 630, 660, 840, 1008, 1560, 1980, 2340, 3120, 3960, 4620, 4680, 6120, 6240, 7920, 9240, 10920, 11880, 12240, 13860, 16380, 18480, 19800, 21840, 23760, 27720, 32760, 36960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Every highly abundant number (A002093) is either in this sequence or A181311. Although it appears that dividing any term by its largest prime factor produces another highly abundant number, this conjecture fails for 2942007868800, the 527th term. LINKS Amiram Eldar, Table of n, a(n) for n = 1..5708 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, 37000}]; seq (* Amiram Eldar, Jan 14 2022 *) CROSSREFS Cf. A002093, A181311. Sequence in context: A229362 A249685 A343731 * A330006 A288784 A322164 Adjacent sequences:  A181309 A181310 A181311 * A181313 A181314 A181315 KEYWORD nonn,changed AUTHOR T. D. Noe, Oct 13 2010 STATUS approved

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Last modified January 23 13:38 EST 2022. Contains 350511 sequences. (Running on oeis4.)