All sequences can have more than one interpretation.  I believe this is the most elegant for given sequence.

Number each term of the sequence 1, 2, 3, ...

The prime numbered terms are given the values 1, 2, 3, ...
(The second term is 1, the third term is 2, the fifth term is 3, etc)

Factor the composite term numbers and multiply the values of these terms.   The 9th term is 4 because 9=3*3 and 4=2*2.  The 14th term is 4 because 14=7*2 and 4=4*1.  This is consistant, although if Tristan had given the 15th term it really would have been the clincher.  

With this interpretation the 15th term is 6 because 15=3*5 and 6=2*3.  15 is the smallest number that is the product of two distinct primes besides 2.