# Removing a element from list when obeying a certain condition

Well, I have the following code:

Select[PowersRepresentations[n, a, b],
DuplicateFreeQ[#] && ! MemberQ[#, 0] &]


This code finds PowersRepresentations a makes a list of the solution. Then DuplicateFreeQ[#] and MemberQ[#, 0] remove the ones that contain a duplicate or a $$0$$.

Question: I want to add to the Select option that when a certain number shows up once in the entire list that element must be removed.

Example 1:

In:=Select[PowersRepresentations[206, 3, 2],
DuplicateFreeQ[#] && ! MemberQ[#, 0] &]

Out={{1, 3, 14}, {1, 6, 13}, {2, 9, 11}, {5, 9, 10}, {6, 7, 11}}


We can see that the numbers $$2$$, $$3$$, $$5$$, $$7$$, $$10$$, $$13$$ and $$14$$ turn up once. So the sets where they turn up must be removed from the list. So the code must give the following output:

{}


Example 2:

In:=Select[PowersRepresentations[965, 3, 2],
DuplicateFreeQ[#] && ! MemberQ[#, 0] &]

Out={{1, 8, 30}, {4, 7, 30}, {4, 18, 25}, {6, 20, 23}, {8, 15, 26}, {9,
10, 28}, {9, 20, 22}, {10, 17, 24}, {12, 14, 25}, {15, 16, 22}}


We can see that the numbers $$1$$, $$6$$, $$7$$, $$12$$, $$16$$, $$17$$, $$18$$, $$23$$, $$24$$, $$26$$ and $$28$$ turn up once. So the sets where they turn up must be removed from the list. So the code must give the following output:

{{9, 20, 22}}


ClearAll[f]
f[x_] := Select[Min[Counts[Flatten @ x] /@ #] > 1 &] @ x


Examples:

f @ Select[DuplicateFreeQ[#] && FreeQ[#, 0] &] @ PowersRepresentations[206, 3, 2]

{}

f @ Select[DuplicateFreeQ[#] && FreeQ[#, 0] &] @ PowersRepresentations[965, 3, 2]


{{9, 20, 22}}