Pairwise Products

★★★★★

3.3

3 votes

Math, Medium, Number Theory, Primality test

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Problem

Misha is given a number $N$ . You are required to help Misha determine the summation of the pairwise product of its divisors.

Input format

First line: $T$ denoting the test cases
Next $T$ lines: $N$

Output format

Print the answer for each test case in a separate line.
Constraints

$1 \le T \le 10^{6}$

$1 \le N \le 10^{7}$

Sample Input

2
4
5

Sample Output

14
5

Time Limit: 5

Memory Limit: 256

Source Limit:

Explanation

Sample Case 1: 4 has three divisors - $\big\{1, 2, 4 \big\}$ . Pairwise summation of divisors will be $(1 \times 2) + (2 \times 4) + (1 \times 4) = 14$
Sample Case 2: 5 has three divisors - $\big\{ 1, 5 \big\}$ . Pairwise summation of divisors will be $1 \times 5 = 5$

Contributers:

Prateek Gupta

Saurabh Joshi