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# Square numbers

The square numbers (perfect squares, or just squares), are integers for which the square root is an integer. Each prime in the prime factorization of a square number appears an even number of times.

For example, 144 is a square number, since $\sqrt{144} = \sqrt{2^{4} \cdot 3^2} = 2^{2} \cdot 3^1 = 12$, while 12 is not a square number, since $\sqrt{12} = \sqrt{2^{2} \cdot 3^1} = 2^1 \cdot \sqrt{3} \approx 3.464101615$.

A000290 The squares: a(n) = n^2, n >= 0.

{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, ...}

## Square numbers as figurate numbers

4-sided polygonal numbers.

2-dimensional regular orthotopic numbers.

2-dimensional orthoplicial polytopic numbers.