What a Coincidence!

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Let \(s(n)\) denote the number of positive integers \(k\) less than or equal to \(n\) such that for all positive integers \(d\) satisfying \(1 < d < k\), we have \(d^2 \not| k\). Let \(t(n)\) denote the number of positive integers \(k\) less than or equal to \(n\) such that \(\gcd(k, n) = 1\). Find the least positive integer \(a\) such that \[20s(a) - t(20.13a) = 0 \]

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