TI-BASIC, 12 bytes

2=sum(not(fPart(Ans/randIntNoRep(1,Ans

Pretty straightforward. randIntNoRep( gives a random permutation of all integers from 1 to Ans.

This bends the rules a little; because lists in TI-BASIC are limited to 999 elements I interpreted

assume that the input can be stored in your data type

as meaning that all datatypes can be assumed to accommodate the input. Works fine for input of 1 to 255.

A 17-byte solution which more clearly complies with the rules:

2=Σ(not(fPart(Ans/A)),A,1,Ans

TI-BASIC, 12 bytes

2=sum(not(fPart(Ans/randIntNoRep(1,Ans

Pretty straightforward. randIntNoRep( gives a random permutation of all integers from 1 to Ans.

This bends the rules a little; because lists in TI-BASIC are limited to 999 elements I interpreted

assume that the input can be stored in your data type

as meaning that all datatypes can be assumed to accommodate the input. OP agrees with this interpretation.

A 17-byte solution which actually works up to 10^12 or so:

2=Σ(not(fPart(Ans/A)),A,1,Ans

TI-BASIC, 12 bytes

2=sum(not(fPart(Ans/randIntNoRep(1,Ans

Pretty straightforward. randIntNoRep( gives a random permutation of all integers from 1 to Ans.

This bends the rules a little; because lists in TI-BASIC are limited to 999 elements I interpreted

assume that the input can be stored in your data type

as meaning that all datatypes can be assumed to accommodate the input.

TI-BASIC, 12 bytes

2=sum(not(fPart(Ans/randIntNoRep(1,Ans

Pretty straightforward. randIntNoRep( gives a random permutation of all integers from 1 to Ans.

This bends the rules a little; because lists in TI-BASIC are limited to 999 elements I interpreted

assume that the input can be stored in your data type

as meaning that all datatypes can be assumed to accommodate the input. Works fine for input of 1 to 255.

A 17-byte solution which more clearly complies with the rules:

2=Σ(not(fPart(Ans/A)),A,1,Ans

TI-BASIC, 12

2=sum(not(fPart(Ans/randIntNoRep(1,Ans

Pretty straightforward. randIntNoRep( gives a random permutation of all integers from 1 to Ans.

This bends the rules a little; because lists in TI-BASIC are limited to 999 elements I interpreted

assume that the input can be stored in your data type

as meaning that all datatypes can be assumed to accommodate the input.

TI-BASIC, 12 bytes

2=sum(not(fPart(Ans/randIntNoRep(1,Ans

Pretty straightforward. randIntNoRep( gives a random permutation of all integers from 1 to Ans.

This bends the rules a little; because lists in TI-BASIC are limited to 999 elements I interpreted

assume that the input can be stored in your data type

as meaning that all datatypes can be assumed to accommodate the input.