Easy methods to adress the # Map variable by way of a perform.

Contemplate the next perform:

sf3[n_,fun_]:=Map[Map[fun[#]&,Vary[Floor[n/#]]]&,Vary[n]]

Now

sf3[4,# &]

returns

{{1, 2, 3, 4}, {1, 2}, {1}, {1}}

as anticipated.

Additionally,

sf3[4, Floor[4/#] &]

returns

{{4, 2, 1, 1}, {4, 2}, {4}, {4}}

as anticipated.

I need to know the right way to handle the internal map variable such that I can create:

{ 
{Flooring[4/1], Flooring[4/2], Flooring[4/3], Flooring[4/4]},
{Flooring[2/1], Flooring[2/2]},
{Flooring[1/1]},
{Flooring[1/1]}
}

So, the

Flooring[4/#] in sf3[4, Floor[4/#] &] 

ought to be one thing like

Flooring[Inner#/#].

?