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 $B\ge 2$.

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 $p_k\le B$. 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