What is the the role of the two a’s in “we planned to meet a few times a year”?

How can I rewrite this sentence without the two a’s?

We planned to meet a few times a year.

I think this would be the best way to show the role that the two a’s play in the sentence.

A few can be replaced with several, and the second a can be replaced with per, each or every.

The usage stats are as follows:

                              BNC    COCA    Google

a few times a year             3      83    16.60M
a few times per year           -       5     2.71M
a few times each year          -      10     1.90M
a few times every year         -       1     0.72M
several times a year          15     159    23.10M
several times per year         -       5     2.19M
several times each year        1      16     3.98M
several times every year       -       2     1.07M

(BNC is the British National Corpus, and COCA is the Corpus of Contemporary American English.)

You could say

We planned to meet a few times each year.

or

We planned to meet a few times every year.

The second sentence is probably more common and less formal.