Mock AIME 5 2005-2006 Problems/Problem 11

Problem

Let $A$ be a subset of consecutive elements of $S = \{n, n+1, \ldots, n+999\}$ where $n$ is a positive integer. Define $\mu(A) = \sum_{k \in A} \tau(k)$, where $\tau(k) = 1$ if $k$ has an odd number of divisors and $\tau(k) = 0$ if $k$ has an even number of divisors. For how many $n \le 1000$ does there exist an $A$ such that $|A| = 620$ and $\mu(A) = 11$? ($|X|$ denotes the cardinality of the set $X$, or the number of elements in $X$)

Solution

Solution

See also

Mock AIME 5 2005-2006 (Problems, Source)
Preceded by
Problem 10
Followed by
Problem 12
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