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MathNet 2014 Question 62

Math Olympiad Vault · MathNet 2014

Question 62

For a positive integer $n$ denote by $s(n)$ the sum of all positive divisors of $n$ and by $d(n)$ the number of positive divisors of $n$. Determine all positive integers $n$ such that
$$
s(n) = n + d(n) + 1.
$$
(Nikola Adžaga)