A181312 Highly abundant numbers k whose largest prime factor is greater than log(k).

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

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

Author

T. D. Noe, Oct 13 2010

Status

approved