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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
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
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
Sequence in context: A229362 A249685 A343731 * A373320 A330006 A288784
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 13 2010
STATUS
approved