A068546 Numbers k such that k*tau(k)>4*prime(k).

840, 1260, 1440, 1680, 1800, 1980, 2016, 2100, 2160, 2340, 2400, 2520, 2640, 2700, 2880, 3024, 3120, 3240, 3360, 3600, 3696, 3780, 3960, 4032, 4080, 4200, 4320, 4368, 4536, 4560, 4620, 4680, 4752, 4800, 5040, 5280, 5400, 5460, 5520, 5544, 5616, 5670

Offset: 1

Author

Benoit Cloitre, Mar 22 2002

Keywords

• easy
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

R:= NULL: count:= 0: p:= 0:
for n from 1 while count < 100 do
  p:= nextprime(p);
  if n * numtheory:-tau(n) > 4 * p then R:= R, n; count:= count+1;  fi;
od:
R; # Robert Israel, May 14 2025

Mathematica

Select[Range[6000],# DivisorSigma[0,#]>4 Prime[#]&] (* Harvey P. Dale, Sep 12 2020 *)