OMCC 2010 Problem 1

Denote by $S(n)$ the sum of the digits of the positive integer $n$ . Find all the solutions of the equation $n(S(n)-1)=2010.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.