Guess the sequence

I wanted to post in the entertaining puzzles , but not enough karma. Therefore, I will write in my blog.

Guess what the next function f counts on a set of natural numbers. Here are its first 40 values:
f (1) = 0
f (2) = + infinity (or undefined)
f (3) = f (4) = 2
f (5) = f (6) = ... = f (13) = 3
f (14) = f (15) = ... = f (40) = 4

If difficulties arise, then I will give some clues.
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Update. Tips are not needed. In the comments already have an answer!