Powerful number

A kind of number

About Powerful number

A powerful number is a positive integer such that every prime appearing in its factorization has exponent at least 2. So 4=2², 8=2³, 9=3², 16=2⁴, 25=5² are powerful; 6=2×3 is not.

Key features

  • Also called "squareful" (all prime factors squared or higher).
  • 1 is considered powerful by convention.

Examples:

1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100

Further reading