Python | sympy.divisor_sigma() method

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With the help of sympy.divisor_sigma() method, we can find the divisor function $\sigma_k(n)$ 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 