The mass ratio that makes this coupled oscillator's dimensionless frequency exactly 1 is (sqrt(1729)-1)/36, so the Hardy-Ramanujan number 1729 appears in the solution.
Kanigel, The Man Who Knew Infinity: A Life of the Genius Ramanujan
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Ramanujan's oscillator
The mass ratio that makes this coupled oscillator's dimensionless frequency exactly 1 is (sqrt(1729)-1)/36, so the Hardy-Ramanujan number 1729 appears in the solution.