Use of the indefinite article before a day of the week

Can we use the indefinite article before the name of a day of the week?

I was born on a Sunday.

Or

I was born on Sunday.

Which one is more suitable and correct?

Solution 1:

You should use the indefinite article, otherwise you run the risk of suggesting you were born last Sunday.

Interestingly, when we talk about months, we do not use indefinite articles, despite the fact that months seem to be quite analogous to days (they are both names or indexicals used recurringly to denote intervals of time). One does not say, for example, "I was born in an August." Why this should be the case is an interesting question and may have to do with the difference in prepositions used for days ("on") versus months ("in").