login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181312 Highly abundant numbers k whose largest prime factor is greater than log(k). 2

%I

%S 1,2,3,4,6,10,12,18,20,30,42,60,84,90,120,168,210,336,420,504,630,660,

%T 840,1008,1560,1980,2340,3120,3960,4620,4680,6120,6240,7920,9240,

%U 10920,11880,12240,13860,16380,18480,19800,21840,23760,27720,32760,36960

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

%C 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.

%H Amiram Eldar, <a href="/A181312/b181312.txt">Table of n, a(n) for n = 1..5708</a>

%t 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 *)

%Y Cf. A002093, A181311.

%K nonn

%O 1,2

%A _T. D. Noe_, Oct 13 2010

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 21 19:42 EDT 2022. Contains 353929 sequences. (Running on oeis4.)