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Omni-MATH / For each positive integer n, let k(n) be the number of ones in the binary representation of 2023⋅n. What is the minimum value of k(n)?

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problem

For each positive integer nn, let k(n)k(n) be the number of ones in the binary representation of 2023⋅n2023 \cdot n. What is the minimum value of k(n)k(n)?
Plain-text mathematical notation (without MathML)
For each positive integer n, let k(n) be the number of ones in the binary representation of 2023⋅n. What is the minimum value of k(n)?
Original LaTeX notation
For each positive integer $n$, let $k(n)$ be the number of ones in the binary representation of $2023 \cdot n$. What is the minimum value of $k(n)$?

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