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OlympiadBench / 1945 / For a finite set A of positive integers, we call a partition of A into two…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

For a finite set AA of positive integers, we call a partition of AA into two disjoint nonempty subsets A1A_{1} and A2A_{2} 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 2015 good partitions.
Plain-text mathematical notation (without MathML)
For a finite set A of positive integers, we call a partition of A into two disjoint nonempty subsets A₁ and A₂ 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, we call a partition of $A$ into two disjoint nonempty subsets $A_{1}$ and $A_{2}$ 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.

answer type

Numerical

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID
1945
task_id
42df09d2-ee90-57c0-986d-31693b48ebba
task_key
OE~5fTO~5fmaths~5fen~5fCOMP--train--1945
task_revision_id
4
config / split
OE_TO_maths_en_COMP / train

Official source

initial import