Source: www.grammarcheck.net
Writing Tip: A Couple of Usage Questions to Ponder
This came from a conscientious author:
Question: I was taught to say a couple of weeks, but I’m hearing and reading the term a couple weeks a lot lately. To me (and other people I’ve asked) that sounds odd. Are both statements acceptable? – Sue

More than a couple of pens and pencils
In answer to your question, Sue, my research offered a variety of opinions. Here’s what I concluded from what I read:
In formal writing, it’s better to say “a couple of” (e.g., a couple of weeks passed). While saying “a couple” isn’t wrong, it’s not readily accepted except in dialogue and highly informal writing. Context rules.
Also there’s disagreement if “couple” always refers to two. Can it be used to mean something less specific? I like the comment below found in a language blog that posed the same question.
Dictionaries define the meaning of a word not necessarily its usage. I speak British English and will happily use a phrase such as “a couple of miles” to imply “not only that the distance is short but that its exact measure is unimportant.” If I go into a pub for “a couple of drinks” I have not limited myself to two (unfortunately). It is a flexible concept. As in all things, context rules.
Yes, I agree that this phrase can be used to indicate vagueness and not necessarily mean two. However, I contend that writing be as specific as possible, so I’d favor stating numbers instead of a “wobbly” reference such as “couple” or “couple of.” Again, context rules.
What are your thoughts? Should “a couple of” be the standard as I suggest? Does the phrase have to mean “two” in your book?