galois.is_smooth

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

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

Parameters¶

n: int¶: An integer.
B: int¶: The smoothness bound $B \geq 2$ .

Returns¶

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

See also

factors, is_powersmooth

Notes¶

An integer $n$ with prime factorization $n = p_{1}^{e_{1}} \dots p_{k}^{e_{k}}$ is $B$ -smooth if $p_{k} \leq B$ . The 2-smooth numbers are the powers of 2. The 5-smooth numbers are known as regular numbers. The 7-smooth numbers are known as humble numbers or highly composite numbers.

Examples¶

In [1]: galois.is_smooth(2**10, 2)
Out[1]: True

In [2]: galois.is_smooth(10, 5)
Out[2]: True

In [3]: galois.is_smooth(12, 5)
Out[3]: True

In [4]: galois.is_smooth(60**2, 5)
Out[4]: True