Consider the number PowerSmooth(1000000) with the 2 factors removed; e.g. in pari-gp:

Code:

PowerSmooth(B1)= result=1; forprime(p=3, B1, result *= p^floor(log(B1)/log(p))); return(result)
PowerSmooth(1000000)

This number, in binary, has 720737 bits set to 1 ("binary hamming weight", hammingweight() in pari-gp).

The puzzle is: find a multiple of this number that has a Hamming Weight <= 710000. (or, How low a HW multiple can you find?)

Thanks! :)