Square numbers

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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

2√ 144

=

2√ 2 4 ⋅ 3 2

= 2 2 ⋅ 3 1 = 12

, while 12 is not a square number, since

2√ 12

=

2√ 2 2 ⋅ 3 1

= 2 1 ⋅

2√ 3

≈ 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, ...}