2525"""
2626
2727
28- def find_primes (n : int ) -> list [int ]:
28+ def find_primes (n : int ) -> list [int ]:
2929 """
3030 Returns a list of all primes less than or equal to n
3131 >>> find_primes(19)
@@ -39,7 +39,7 @@ def find_primes(n : int) -> list[int]:
3939 return [i for i in range (2 , n + 1 ) if sieve [i ]]
4040
4141
42- def find_prime_factorizations (n : int ) -> list [dict [int , int ]]:
42+ def find_prime_factorizations (n : int ) -> list [dict [int , int ]]:
4343 """
4444 Returns a list of prime factorizations of 2...n, with prime
4545 factorization represented as a dictionary of (prime, exponent) pairs
@@ -59,7 +59,7 @@ def find_prime_factorizations(n : int) -> list[dict[int, int]]:
5959 return prime_factorizations
6060
6161
62- def num_divisors_of_square (prime_factorization : dict [int , int ]) -> int :
62+ def num_divisors_of_square (prime_factorization : dict [int , int ]) -> int :
6363 """
6464 Returns the number of divisors of n * n, where n is the
6565 number represented by the input prime factorization
@@ -72,7 +72,7 @@ def num_divisors_of_square(prime_factorization : dict[int, int]) -> int:
7272 return num_divisors
7373
7474
75- def solution (target : int = 1000 ) -> int :
75+ def solution (target : int = 1000 ) -> int :
7676 """
7777 Returns the smallest n with more than 'target' solutions
7878 >>> solution()
@@ -89,5 +89,6 @@ def num_solutions(n):
8989 if num_solutions (i ) > target :
9090 return i
9191
92+
9293if __name__ == "__main__" :
9394 print (f"{ solution () = } " )
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