Python| sympy.udivisor_sigma() 方法

借助sympy.udivisor_sigma()方法，我们可以计算酉除数函数$\sigma_k^*(n)$对于任何正整数n 。 udivisor_sigma(n, k)等于n的所有酉除数之和的k次幂或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.

示例 #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

输出：

udivisor_sigma(12) =  20

示例 #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)) 

输出：

udivisor_sigma(18) =  410