Problem p02061 - Generation 1

Orig Description

B: Twice of oneself
Problem
You are given Q queries. For each query, you are given a positive integer N, and you need to find the number of positive integers M that satisfy the following two conditions:
2 \leq M \leq N
The sum of the proper divisors of M (i.e. the divisors of M other than M itself) is at least twice as large as M.
Input Format
The input is given in the following format:
Q
N_1
N_2
:
N_Q
The first line contains the number of queries, Q.
The following N lines contain one positive integer N per query.
Constraints
1 \leq Q \leq 10^5
2 \leq N_i \leq 10^5 (1 \leq i \leq Q)
Output Format
For each given N, output the number of positive integers M that satisfy the above two conditions, separated by a newline.
Sample Input
3
43
9
24
Sample Output
11
0
5
For N=24, the five possible values of M are 12, 16, 18, 20, and 24.

Extracted Specification

Canonicalized Input Description:

An integer Q (1 ≤ Q ≤ 10^5), representing some quantity.
A list of Q integers, where each integer Ni (2 ≤ Ni ≤ 10^5).

### Example Input:

```
3
43
9
24
```

### Function Signature:
Write a function f(inputs) that takes in the input.
def f(inputs: List[int]):
    '''
    inputs: a list of integers
    '''

Test Case Generator

To create a test case generator for the given problem "Twice of oneself", we need to generate multiple queries, each with a positive integer \(N\) within the specified constraints. 

Here's a Python function to generate such test cases:

```python
import random

def generate_test_case():
    Q = random.randint(1, 10**5)  # Number of queries
    
    queries = [random.randint(2, 10**5) for _ in range(Q)]  # List of N values for each query
    
    return Q, queries

# Function to print out the test case in the required format
def print_test_case():
    Q, queries = generate_test_case()
    print(Q)
    for query in queries:
        print(query)

print_test_case()
```

### Explanation of the Generator:

1. **Number of Queries (`Q`)**: 
   - Randomly select an integer between 1 and \(10^5\).

2. **List of Queries (`queries`)**:
   - For each query, randomly select an integer \(N\) between 2 and \(10^5\).

This generator will create a test case that meets the input format and constraints specified in the problem statement. 

### Example Output

Running the `print_test_case()` function might produce an output like this:

```
3
43
9
24
```

This output represents three test queries with \(N\) values of 43, 9, and 24, respectively. The number of queries \(Q\) is 3. 

### Note:
- The random values ensure a wide range of test cases, helping to thoroughly test the solution's efficiency and correctness.
- To ensure reproducibility, you can set a seed for the random number generator using `random.seed(seed_value)`.

Feel free to adjust the constraints or add additional logic if specific edge cases need to be tested.

Extract Arguments

def extract_arguments(fh):
    Q = int(fh.readline().strip())
    N = [int(fh.readline().strip()) for _ in range(Q)]
    return (Q, N)