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Omni-MATH / Let T be the set of numbers of the form 2^(a)3^(b) where a and b are integers satisfying 0≤a,b≤5. How many subsets S of T have the property that if n is in S then all positive inte…

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problem

Let TT be the set of numbers of the form 2a3b2^{a} 3^{b} where aa and bb are integers satisfying 0≤a,b≤50 \leq a, b \leq 5. How many subsets SS of TT have the property that if nn is in SS then all positive integer divisors of nn are in SS ?
Plain-text mathematical notation (without MathML)
Let T be the set of numbers of the form 2^(a)3^(b) where a and b are integers satisfying 0≤a,b≤5. How many subsets S of T have the property that if n is in S then all positive integer divisors of n are in S ?
Original LaTeX notation
Let $T$ be the set of numbers of the form $2^{a} 3^{b}$ where $a$ and $b$ are integers satisfying $0 \leq a, b \leq 5$. How many subsets $S$ of $T$ have the property that if $n$ is in $S$ then all positive integer divisors of $n$ are in $S$ ?

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Source and history

task_id
7ab1ab72-c7d4-5636-9a7f-bc8371397cda
task_key
test--7ab1ab72-c7d4-5636-9a7f-bc8371397cda
task_revision_id
1
config / split
/ test

Official source

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