A181311 Highly abundant numbers k whose largest prime factor is less than log(k).

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

Amiram Eldar, Table of n, a(n) for n = 1..4292

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

Cf. A002093, A181312.

Sequence in context: A342018 A369035 A055065 * A083496 A125991 A028589

Adjacent sequences: A181308 A181309 A181310 * A181312 A181313 A181314

Keyword

nonn

Author

T. D. Noe, Oct 13 2010

Status

approved