Algorithm to find unique prime factors (#9935)

* algorithm to find unique prime factors * Update prime_factors.py * Update prime_factors.py * Update prime_factors.py --------- Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

Author: Mary-0165

maths/prime_factors.py

@@ -47,6 +47,46 @@ def prime_factors(n: int) -> list[int]:
  return factors
 
 
+def unique_prime_factors(n: int) -> list[int]:
+ """
+ Returns unique prime factors of n as a list.
+
+ >>> unique_prime_factors(0)
+ []
+ >>> unique_prime_factors(100)
+ [2, 5]
+ >>> unique_prime_factors(2560)
+ [2, 5]
+ >>> unique_prime_factors(10**-2)
+ []
+ >>> unique_prime_factors(0.02)
+ []
+ >>> unique_prime_factors(10**241)
+ [2, 5]
+ >>> unique_prime_factors(10**-354)
+ []
+ >>> unique_prime_factors('hello')
+ Traceback (most recent call last):
+ ...
+ TypeError: '<=' not supported between instances of 'int' and 'str'
+ >>> unique_prime_factors([1,2,'hello'])
+ Traceback (most recent call last):
+ ...
+ TypeError: '<=' not supported between instances of 'int' and 'list'
+ """
+ i = 2
+ factors = []
+ while i * i <= n:
+ if not n % i:
+ while not n % i:
+ n //= i
+ factors.append(i)
+ i += 1
+ if n > 1:
+ factors.append(n)
+ return factors
+
+
 if __name__ == "__main__":
  import doctest