... or just considering the even numbers almost all of them are 2 x N where N>2^32 and that gets you to within a hair of "most" and if you add in the odd thirds for which the same is true you get a bound of 2/3 - epsilon.

It's a bit more subtle than that -- most n>2^32 are not prime in which case 2 x n has more factorizations you would have to check.

(Just by way of example, for n=2^33, 2n=2^34 but also =2^17*2^17)