galois.is_powersmooth

galois.is_powersmooth(n: int, B: int) → bool

Determines if the integer $n$ is $B$ -powersmooth.

Parameters:¶

Returns:¶

True if $n$ is $B$ -powersmooth.

See also

Notes

An integer $n$ with prime factorization $n = p_{1}^{e_{1}} \dots p_{k}^{e_{k}}$ is $B$ -powersmooth if $p_{i}^{e_{i}} \leq B$ for $1 \leq i \leq k$ .

Examples

Comparison of $B$ -smooth and $B$ -powersmooth. Necessarily, any $n$ that is $B$ -powersmooth must be $B$ -smooth.

In [1]: galois.is_smooth(2**4 * 3**2 * 5, 5)
Out[1]: True

In [2]: galois.is_powersmooth(2**4 * 3**2 * 5, 5)
Out[2]: False