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Sum Squares

There are numbers that are equal to the square of the sum of their digits. The two smallest are 0 and 1. For 287, this is almost the case, namely: (2 + 8 + 7)² = 289.

Challenger

What is the next number with this special property?

Mastermind

What is the largest number with this property? Answer 999999999999 (12x9) if there are infinitely many.