How do we define the function near the end of my post?

Question

Suppose I have two sets $F_{1,n}$ and $F_{2,n}$ written as:

F1[t_] := 
 F1[t] = Sort[
   N[DeleteDuplicates[
     Flatten[Sqrt[
       Range[Ceiling[((t)!)], Floor[4 (t!)]]/((t!))]]]]]

F2[t_] := 
 F2[t] = Sort[
   N[DeleteDuplicates[
     Flatten[Table[Sqrt[Range[s, 4 s]/s], {s, 1, t}]]]]]

And we have

\[CapitalDelta]F1[t_] := \[CapitalDelta]F1[t] = Differences[F1[t]]
\[CapitalDelta]F2[t_] := \[CapitalDelta]F2[t] = Differences[F2[t]]

H[t_]:=H[t]=t/Total[t]

E1[t_] := 
 E1[t] = -Total[
    H[\[CapitalDelta]F1[t]] Log[2, H[\[CapitalDelta]F1[t]]]]
E2[t_] := 
 E2[t] = -Total[
    H[\[CapitalDelta]F2[t]] Log[2, H[\[CapitalDelta]F2[t]]]]

T1[x_] := 
 T1[x] = (2^(Mean[F1[x]]) (2^(E1[x + 1] - E1[x]))/(Length[F1[x + 1]]/
       Length[F1[x]]))
T2[x_] := 
 T2[x] = (2^
     Mean[F2[x]] (2^(E2[x + 1] - E2[x]))/(Length[F2[x + 1]]/
       Length[F2[x]])) 

How do we define:

$$\sum\limits_{n=1}^{z}\sup\left\{|F_{2,j}|:j\in\mathbb{N},T2[j]\ge T1[n]\right\}$$

Attempt

I started with the code:

F2 \@ NSolve[T2[j] > T1[n], {j}, Integers]

but immedietely get:

Range::range: Range specification in Range[16 s,49 s] does not have appropriate bounds.

How fix this and complete the solution? Is there better code to be used?