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# Help

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If we let $$f(n)$$ denote the sum of all the positive divisors of the integer $$n$$, how many integers $$i$$ exist such that $$1 \le i \le 2010$$ and $$f(i) = 1 + \sqrt{i} + i$$?

Jul 11, 2020

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Because of the sqrt(i) term, i must be a perfect square.  There are 44 perfect squares in the range 1, 2, 3, ..., 2010, so there are 44 vaues of i.

Jul 11, 2020