Python | sympy.totient() method

Python sympy | sieve.totientrange() method

Last Updated : 27 Aug, 2019

With the help of sympy.sieve.totientrange() method, we can generate all totient numbers for a given range [a, b). It returns a type generator object which can be converted to a list for further operations.

Syntax: sieve.totientrange(a, b)
Parameters:
a – It denotes the start of the range. It is inclusive.
b – It denotes the end of the range. It is not inclusive.
Returns: The method returns a type generator object.

Example #1:

# import sympy  
from sympy import sieve 
  
# Use sieve.totientrange() method  
totient_gen = sieve.totientrange(1, 10)  
totient_list = list(totient_gen) 
      
print("Totient numbers for the range of numbers [1, 10) : {}".format(totient_list))   

Output:

Totient numbers for the range of numbers [1, 10) : [1, 1, 2, 2, 4, 2, 6, 4, 6]

Example #2:

# import sympy  
from sympy import sieve 
  
# Use sieve.totientrange() method  
totient_gen = sieve.totientrange(8, 20)  
totient_list = list(totient_gen) 
      
print("Totient numbers for the range of numbers [8, 20) : {}".format(totient_list))       

Output:

Totient numbers for the range of numbers [8, 20) : [4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18]

Python | sympy.totient() method

rupesh_rao

Improve

Article Tags :

Python
SymPy

Practice Tags :

python

Similar Reads

Python | sympy.totient() method

With the help of sympy.totient() method, we can find Euler totient function or phi(n) of a given integer. Euler totient function is the number of positive integers less than or equal to a given integer that are relatively prime to it. In other words, it is the number of integers k in the range 1

Python | sympy.reduced_totient() method

With the help of sympy.reduced_totient() method, we can find the Carmichael reduced totient function or lambda(n) in SymPy. reduced_totient(n) or [Tex]\lambda(n)[/Tex] is the smallest m > 0 such that [Tex]k^m \equiv 1 \mod n[/Tex] for all k relatively prime to n. Syntax: reduced_totient(n) Parame

Python sympy | sieve.extend_to_no() method

With the help of sympy.sieve.extend_to_no() method, we can extend the sieve to include the ith prime number. Note: The list is extended by 50% if it is too short, so it is likely that it will be longer than requested. Syntax: sieve.extend_to_no(i) Parameter: i - It denotes that the sieve is extended

Python sympy | sieve.extend() method

With the help of sympy.sieve.extend() method, we can grow the sieve to cover all the prime numbers less than equal to a given natural number. Syntax: sieve.extend(N) Parameter: N - It denotes the number up to which the sieve is extended. Returns: The function does not return anything. Example #1: #

Python sympy | sieve.search() method

With the help of sympy.sieve.search() method, we can find the indices i, j of the primes that bound a given number. If the given number is prime then i == j. Syntax: sieve.search(n) Parameter: n - It denotes the number whose bounding prime indices is found. Returns: Returns a tuple containing the bo

Python sympy | sieve.primerange() method

With the help of sympy.sieve.primerange() method, we can generate all prime numbers for a given range [a, b). It returns a type generator object which can be converted to a list for further operations. Syntax: sieve.primerange(a, b) Parameters: a - It denotes the start of the range. It is inclusive.

Python sympy | sieve.mobiusrange() method

With the help of sympy.sieve.mobiusrange() method, we can generate the mobius numbers for a given range [a, b). It returns a type generator object which can be converted to a list for further operations. Syntax: sieve.mobiusrange(a, b) Parameters: a - It denotes the start of the range. It is inclusi

Python | sympy.randprime() method

With the help of sympy.randprime() method, we can find a random prime number in the range [a, b), where a and b are parameters to the method. Syntax: randprime(a, b) Parameter: a - It denotes the start of the range. It is inclusive. b - It denotes the end of the range. It is not inclusive. Returns:

Python | sympy.subfactorial() method

With the help of sympy.subfactorial() method, we can find the Subfactorial of a number in SymPy. Subfactorial of a number is given by - [Tex] !n = \begin{cases} 1 & n = 0 \\ 0 & n = 1 \\ (n-1)(!(n-1) + !(n-2)) & n > 1 \end{cases} [/Tex] Syntax: subfactorial(n) Parameter: n - It denote

Python | sympy.divisor_sigma() method

With the help of sympy.divisor_sigma() method, we can find the divisor function [Tex]\sigma_k(n)[/Tex] 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