VyxalVyxal j, 108 bytes
∞'dǏG7<;?ẎλdǏG7<;ȯ ∞ # All positive integers ' ; # Filter by d λ ;ȯ # Double (to handle 1, which hasFirst non primenumbers factors)where ǏG dǏG # MaxMaximum of prime factors 7< # Is lessLess than 7 ?Ẏ # First n