Python | sympy.divisor_sigma() method

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

Syntax: divisor_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 divisors of n raised to the power of k.

Example #1:

# import divisor_sigma() method from sympy
from sympy.ntheory import divisor_sigma

n = 8

# Use divisor_sigma() method
divisor_sigma_n = divisor_sigma(n)

print("divisor_sigma({}) =  {} ".format(n, divisor_sigma_n))
# 1 ^ 1 + 2 ^ 1 + 4 ^ 1 + 8 ^ 1 = 15

Output:

divisor_sigma(8) =  15 

Example #2:

# import divisor_sigma() method from sympy
from sympy.ntheory import divisor_sigma

n = 15
k = 2

# Use divisor_sigma() method
divisor_sigma_n = divisor_sigma(n, k)

print("divisor_sigma({}, {}) =  {} ".format(n, k, divisor_sigma_n))
# 1 ^ 2 + 3 ^ 2 + 5 ^ 2 + 15 ^ 2 = 260

Output:

divisor_sigma(15, 2) =  260