Python | sympy.udivisor_sigma() method

With the help of sympy.udivisor_sigma() method, we can calculate the unitary divisor function for any positive integer n. udivisor_sigma(n, k) is equal to sum of all the unitary divisors of n raised to the power of k or sum([x**k for x in udivisors(n)]).

Syntax: udivisor_sigma(n, k) Parameter: n – It denotes an integer. k – It denotes an integer(optional). Default for k is 1. Returns: Returns the sum of all the unitary divisors of n raised to the power of k.

Example #1:

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

n = 12

# Use udivisor_sigma() method
udivisor_sigma_n = udivisor_sigma(n)

print("udivisor_sigma({}) =  {} ".format(n, udivisor_sigma_n))
# 1 ^ 1 + 3 ^ 1 + 4 ^ 1 + 12 ^ 1 = 20

Output:

udivisor_sigma(12) =  20

Example #2:

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

n = 18
k = 2

# Use udivisor_sigma() method
udivisor_sigma_n = udivisor_sigma(n, k)

print("udivisor_sigma({}) =  {} ".format(n, udivisor_sigma_n))

Output:

udivisor_sigma(18) =  410