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Omni-MATH / For a finite set A of positive integers, a partition of A into two disjoint nonempty subsets A₁ and A₂ is textit{good} if the least common multiple of the elements in A₁ is equal t…

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problem

For a finite set AA of positive integers, a partition of AA into two disjoint nonempty subsets A1A_1 and A2A_2 is $\textit{good}$ if the least common multiple of the elements in A1A_1 is equal to the greatest common divisor of the elements in A2A_2. Determine the minimum value of nn such that there exists a set of nn positive integers with exactly 20152015 good partitions.
Plain-text mathematical notation (without MathML)
For a finite set A of positive integers, a partition of A into two disjoint nonempty subsets A₁ and A₂ is $\textit{good}$ if the least common multiple of the elements in A₁ is equal to the greatest common divisor of the elements in A₂. Determine the minimum value of n such that there exists a set of n positive integers with exactly 2015 good partitions.
Original LaTeX notation
For a finite set $A$ of positive integers, a partition of $A$ into two disjoint nonempty subsets $A_1$ and $A_2$ is $\textit{good}$ if the least common multiple of the elements in $A_1$ is equal to the greatest common divisor of the elements in $A_2$. Determine the minimum value of $n$ such that there exists a set of $n$ positive integers with exactly $2015$ good partitions.

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Source and history

task_id
12264810-dafe-55b2-ba24-91c40fd2eb66
task_key
test--12264810-dafe-55b2-ba24-91c40fd2eb66
task_revision_id
1
config / split
/ test

Official source

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