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Omni-MATH / Let C={4,6,8,9,10,…} be the set of composite positive integers. For each n∈C let a_(n) be the smallest positive integer k such that k ! is divisible by n. Determine whether the fol…

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problem

Let C={4,6,8,9,10,…}C=\{4,6,8,9,10, \ldots\} be the set of composite positive integers. For each n∈Cn \in C let ana_{n} be the smallest positive integer kk such that kk ! is divisible by nn. Determine whether the following series converges: ∑n∈C(ann)n\sum_{n \in C}\left(\frac{a_{n}}{n}\right)^{n}
Plain-text mathematical notation (without MathML)
Let C={4,6,8,9,10,…} be the set of composite positive integers. For each n∈C let a_(n) be the smallest positive integer k such that k ! is divisible by n. Determine whether the following series converges: ∑_(n∈C)((a_(n))/(n))^(n)
Original LaTeX notation
Let $C=\{4,6,8,9,10, \ldots\}$ be the set of composite positive integers. For each $n \in C$ let $a_{n}$ be the smallest positive integer $k$ such that $k$ ! is divisible by $n$. Determine whether the following series converges: $$\sum_{n \in C}\left(\frac{a_{n}}{n}\right)^{n}$$

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task_id
8a671765-4c10-5e6e-a85a-23157c3b72ad
task_key
test--8a671765-4c10-5e6e-a85a-23157c3b72ad
task_revision_id
1
config / split
/ test

Official source

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