Definition:Perfect Power

Definition

A perfect power is an integer which can be expressed in the form:

$a^k$

where both $a$ and $k$ are integers with $a \ge 1$ and $k \ge 2$.

Sequence

The sequence of perfect powers begins:

$1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 121, 125, \ldots$

Sources

• Weisstein, Eric W. "Perfect Power." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PerfectPower.html