Counting Tuples solution codechef

Counting Tuples solution codechef

Counting Tuples solution codechef

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You are given an integer $N$ . You have to count the number of distinct tuples $(A, B, C, D)$ with $1 \leq A, B, C, D \leq N$ such that $A \cdot B = C \cdot D$ .

Two tuples, say $(A, B, C, D)$ and $(E, F, G, H)$ are considered to be different if at least one of the following conditions hold true:

$A \neq E$
$B \neq F$
$C \neq G$
$D \neq H$ .

Counting Tuples solution codechef

First line will contain $T$ , number of testcases. Then the testcases follow.
Each testcase contains a single integer on a new line – $N$ , as described in the problem statement

Output Format

For each testcase, output the answer on a new line – the number of tuples as described in the problem statement.

Counting Tuples solution codechef

$1 \leq T \leq 10$
$1 \leq N \leq 10^{6}$

Counting Tuples solution codechef

Counting Tuples solution codechef

15
10950
4831

Counting Tuples solution codechef

Test case $1$ : Following tuples satisfy the given condition:

(1, 1, 1, 1)
(1, 2, 2, 1)
(1, 3, 3, 1)
(2, 1, 1, 2)
(2, 2, 2, 2)
(2, 3, 3, 2)
(3, 1, 1, 3)
(3, 2, 2, 3)
(3, 3, 3, 3)
(1, 2, 1, 2)
(2, 1, 2, 1)
(1, 3, 1, 3)
(3, 1, 3, 1)
(2, 3, 2, 3)
(3, 2, 3, 2)

$A \cdot B = C \cdot D$ holds true for all these tuples.

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