Python | sympy.smoothness() method

With the help of sympy.smoothness() method, we can find smoothness and power-smoothness of a given number. The smoothness of a number is its largest prime factor and the power-smoothness is its largest divisor raised to its multiplicity.

Syntax:
smoothness(n)

Parameter:
n – It denotes the number for which the smoothness and power-smoothness is calculated.

Returns:
Returns a tuple of smoothness and power-smoothness of the given number.

Example #1:

# import smoothness() method from sympy
from sympy.ntheory.factor_ import smoothness

n = 64

# Use smoothness() method
smoothness_n, power_smoothness_n = smoothness(n)

print("The smoothness and power-smoothness of {} is {} and {} respectively".
      format(n, smoothness_n, power_smoothness_n))

Output:

The smoothness and power-smoothness of 64 is 2 and 64 respectively

Example #2:

from sympy.ntheory.factor_ import smoothness

n = 2**4 * 13

# Use smoothness() method
smoothness_n, power_smoothness_n = smoothness(n)

print("The smoothness and power-smoothness of {} is {} and {} respectively".
      format(n, smoothness_n, power_smoothness_n))

Output:

The smoothness and power-smoothness of 208 is 13 and 16 respectively