Pixel brush getting rounded corner

Thanks for looking into this, unfortunately defining a larger square brush won't let me scale it down to one pixel I will essentially have to have two different types of brushes for the type of work I am doing.

I thought by maybe defining a 16px (power of 2) square since that's where the rounded corner begins I would be able to scale it larger and down to one px while retaining it's sharp square edges but even the 16px square brush eventually had the rounded corners when scale up further.

This is very odd cause the top left part of the brush stays sharp and it's only the bottom right that is affected.

That's interesting, but it is still what you'd expect.  You can't really have a true one pixel brush in Photoshop, because the brush tool always uses anti aliasing.   The screenshot below shows the one pixel i stamped with the Pencil tool, and defined as a brush preset.

You can see the zoom ration in the document tab. 

You can also see that even at this tiny size, the outline is already distorted, and the four stamps using that preset with the brush tool depend on where the cursor was placed in relation to the pixel grid.  In fact no two are exactly the same.

I was going to say just use the pencil tool and you'll be good to go, but that loses the bottom right corner as well.

So your best bet might be to load the Legacy brush set, and use the Square Brushes group

Incidentally, even they have some aa, and it defaults to the right and bottom edges, which explains what you are seeing