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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

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