A163569 - OEIS
360, 504, 540, 600, 756, 792, 936, 1176, 1188, 1224, 1350, 1368, 1400, 1404, 1500, 1656, 1836, 1960, 2052, 2088, 2200, 2232, 2250, 2484, 2600, 2646, 2664, 2904, 2952, 3096, 3132, 3348, 3384, 3400, 3500, 3800, 3816, 3996, 4056, 4116, 4248, 4312, 4392
COMMENTS
There is no constraint on which of the three primes is the largest or smallest.
EXAMPLE
360=2^3*3^2*5. 504=2^3*3^2*7. 1188=2^2*3^3*11.
MATHEMATICA
f[n_]:=Sort[Last/@FactorInteger[n]]=={1, 2, 3}; Select[Range[5000], f]
PROG
(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\12)^(1/3), t1=p^3; forprime(q=2, sqrt(lim\t1), if(p==q, next); t2=t1*q^2; forprime(r=2, lim\t2, if(p==r||q==r, next); listput(v, t2*r)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011