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Omni-MATH / Call a positive integer n quixotic if the value of lcm(1,2,3,…,n)⋅((1)/(1)+(1)/(2)+(1)/(3)+…+(1)/(n)) is divisible by 45 . Compute the tenth smallest quixotic integer.

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problem

Call a positive integer nn quixotic if the value of lcm(1,2,3,…,n)⋅(11+12+13+…+1n)\operatorname{lcm}(1,2,3, \ldots, n) \cdot\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{n}\right) is divisible by 45 . Compute the tenth smallest quixotic integer.
Plain-text mathematical notation (without MathML)
Call a positive integer n quixotic if the value of lcm(1,2,3,…,n)⋅((1)/(1)+(1)/(2)+(1)/(3)+…+(1)/(n)) is divisible by 45 . Compute the tenth smallest quixotic integer.
Original LaTeX notation
Call a positive integer $n$ quixotic if the value of $\operatorname{lcm}(1,2,3, \ldots, n) \cdot\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{n}\right)$ is divisible by 45 . Compute the tenth smallest quixotic integer.

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Source and history

task_id
dfef505d-9815-5ea6-bf67-48e05085d412
task_key
test--dfef505d-9815-5ea6-bf67-48e05085d412
task_revision_id
1
config / split
/ test

Official source

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