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 $X$ )

Mock AIME 5 2005-2006 (Problems, Source)
Preceded by Problem 10	Followed by Problem 12
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15

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Mock AIME 5 2005-2006 Problems/Problem 11

Contents

Problem

Solution

Solution

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