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Omni-MATH / A subset S of the set {1,2,…,10} is chosen randomly, with all possible subsets being equally likely. Compute the expected number of positive integers which divide the product of th…

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problem

A subset SS of the set {1,2,…,10}\{1,2, \ldots, 10\} is chosen randomly, with all possible subsets being equally likely. Compute the expected number of positive integers which divide the product of the elements of SS. (By convention, the product of the elements of the empty set is 1.)
Plain-text mathematical notation (without MathML)
A subset S of the set {1,2,…,10} is chosen randomly, with all possible subsets being equally likely. Compute the expected number of positive integers which divide the product of the elements of S. (By convention, the product of the elements of the empty set is 1.)
Original LaTeX notation
A subset $S$ of the set $\{1,2, \ldots, 10\}$ is chosen randomly, with all possible subsets being equally likely. Compute the expected number of positive integers which divide the product of the elements of $S$. (By convention, the product of the elements of the empty set is 1.)

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Source and history

task_id
8190ea4e-8f62-50ed-8233-76e99f771253
task_key
test--8190ea4e-8f62-50ed-8233-76e99f771253
task_revision_id
1
config / split
/ test

Official source

initial import