Create a function that returns the prime factorization of an integer as a sorted list of tuples. Include the multiplicity of each prime in the tuples:
- [(prime_0, mult_0), ..., (prime_k, mult_k)]
- where prime_0 < prime_1 < ... < prime_k
Examples
factorize(4) ➞ [(2, 2)]
factorize(10) ➞ [(2, 1), (5, 1)]
factorize(60) ➞ [(2, 2), (3, 1), (5, 1)]
Notes
- Don't worry about negatives or floats. All inputs will be positive integers.
- 1 is not a prime! Do not include it. You will not be given 1 as an input.
- All inputs will be less than 10,000.