For each positive integer $$k,$$ let $$S_k$$ denote the increasing arithmetic sequence of integers whose first term is 1 and whose common difference is $$k.$$ For example, $$S_3$$ is the sequence $$1,4,7,10,\ldots.$$ For how many values of $$k$$ does $$S_k$$ contain the term 2005?

(第二十三届AIME1 2005 第2题)