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Omni-MATH / Let S be a set of positive integers, such that n∈S if and only if ∑_(d|n,d<n,d∈S)d≤n Find all positive integers n=2^(k)⋅p where k is a non-negative integer and p is an odd prime, s…

Problem

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problem

Let SS be a set of positive integers, such that n∈Sn \in S if and only if ∑d|n,d<n,d∈Sd≤n\sum_{d|n,d<n,d \in S} d \le n Find all positive integers n=2k⋅pn=2^k \cdot p where kk is a non-negative integer and pp is an odd prime, such that ∑d|n,d<n,d∈Sd=n\sum_{d|n,d<n,d \in S} d = n
Plain-text mathematical notation (without MathML)
Let S be a set of positive integers, such that n∈S if and only if ∑_(d|n,d<n,d∈S)d≤n
Find all positive integers n=2^(k)⋅p where k is a non-negative integer and p is an odd prime, such that ∑_(d|n,d<n,d∈S)d=n
Original LaTeX notation
Let $S$ be a set of positive integers, such that $n \in S$ if and only if $$\sum_{d|n,d<n,d \in S} d \le n$$
Find all positive integers $n=2^k \cdot p$ where $k$ is a non-negative integer and $p$ is an odd prime, such that $$\sum_{d|n,d<n,d \in S} d = n$$

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Source and history

task_id
8a729738-35ba-5278-a7d5-676527bee5e9
task_key
test--8a729738-35ba-5278-a7d5-676527bee5e9
task_revision_id
4
config / split
/ test

Official source

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