Given a list of integers, count and return the number of times each value appears as an array of integers.

Sure, here is a Python solution for your problem:

def count_numbers(nums):
    # Create an empty dictionary
    count_dict = {}

    # Iterate over the list of numbers
    for num in nums:
        # If the number is already in the dictionary, increment its count
        if num in count_dict:
            count_dict[num] += 1
        # If the number is not in the dictionary, add it with a count of 1
        else:
            count_dict[num] = 1

    # Convert the dictionary to a list of counts
    counts = list(count_dict.values())

    return counts

This function takes a list of integers as input and returns a list of counts. It uses a dictionary to keep track of the count of each number. The keys of the dictionary are the numbers and the values are their counts. The function iterates over the list of numbers and for each number, it checks if it is already in the dictionary. If it is, it increments its count. If it is not, it adds it to the dictionary with a count of 1. Finally, it converts the dictionary to a list of counts and returns it.