Perfect powers

A perfect power is a positive integer that can be expressed as m^k for integers m > 1 and k ≥ 2. So squares (k = 2), cubes (k = 3), and higher powers are included. 1 is sometimes excluded; 4, 8, 9, 16, 25 are perfect powers.

Key features

• Squares: 4, 9, 16, 25; cubes: 8, 27, 64.
• A number is a perfect power if and only if the gcd of exponents in its prime factorization is greater than 1.
• Not every number is a perfect power: 2, 3, 5, 6, 7, 10 are not.

Examples:

4, 8, 9, 16, 25, 27

Further reading

• Perfect powers on Wikipedia
• Related sequence on OEIS