# A subset here, a subset there ....

Number Theory Level 5

Let $$S(n)$$ be the number of subsets $$\{a,b\}$$ of the set $$\{1,2,3, .... , 1000\}$$ such that $$n | ab$$.

Find $$S(13) - 2*S(31)$$.

Notes:

• The elements $$a$$ and $$b$$ must be distinct.

• By "$$n | ab$$" I mean that $$n$$ divides $$ab$$.

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