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erdos_939.variants.triples

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Are there infinitely many triples of coprime $3$-powerful numbers $a, b, c$ such that $a + b = c$?

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Lean 4 Statement 
theorem erdos_939.variants.triples :
    answer(sorry) ↔ {(a,b,c) | ({a, b, c} : Finset ℕ).Coprime ∧
      (3).Full a ∧ (3).Full b ∧ (3).Full c ∧
      a + b = c}.Infinite
ID: ErdosProblems__939__erdos_939.variants.triples
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