sizeof is an operator in C, and does not need parenthesis any more than pointer operator *. It is true that programmers frequently think of it as a function and use parenthesis.
To begin with, sizeof has two syntaxes: the first, which is the one you seem to refer to, is simply
sizeof expression
where expression involves variables and constants, not types. The second is
sizeof (type)
where the parentheses are mandatory.
Then, even in the first syntax, even if sizeof is listed among the operators, even if it doesn't look any different from "pointer operator ", nonetheless it has strange priority rules. For example
sizeof (T) *x
If it was a regular prefix operator obeying priority and right-to-left evaluation, this would mean: dereference x, cast it to T, and return its size. Instead the C standard forces the compiler to interpret it as: take the size of type T and multiply it by x.
Hilariously I've been down voted, even though you absolutely need sizeof (char) because it's a type. Given char x; sizeof x is fine. I know sizeof is an operator. I've been using C for 40 years.
To begin with, sizeof has two syntaxes: the first, which is the one you seem to refer to, is simply
where expression involves variables and constants, not types. The second is where the parentheses are mandatory.Then, even in the first syntax, even if sizeof is listed among the operators, even if it doesn't look any different from "pointer operator ", nonetheless it has strange priority rules. For example
If it was a regular prefix operator obeying priority and right-to-left evaluation, this would mean: dereference x, cast it to T, and return its size. Instead the C standard forces the compiler to interpret it as: take the size of type T and multiply it by x.