powerful number

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powerful number

Examples (mathematics)
$144000 = 2 7 \times 3 2 \times 5 3 = 2 3 \times 2 4 \times 3 2 \times 5 3 = (2 \times 5) 3 \times (2 2 \times 3) 2$ $144000$ is a powerful number. Every exponent in its prime factorization is larger than 1. It is the product of a square and a cube.

powerful number (plural powerful numbers)

(mathematics) A positive integer $m$ such that for every prime number $p$ dividing $m$ , $p 2$ also divides $m$ . Equivalently, it is the product of a square and a cube.

integer where each prime number dividing it can be squared to still divide it