[Solution] Gcd and Lcm CodeChef Solution | CodeChef Problem Solution 2022

[Solution] Gcd and Lcm CodeChef Solution | CodeChef Problem Solution 2022

You are given an integer N$N$.

You are asked to find total number of integer pairs (A,B)$(A,B)$ such that

• 1≤A,B≤N$1\le A,B\le N$
• A2+B2+gcd2(A,B)+lcm2(A,B)=N$A^2+B^2+gc{d}^2(A,B)+lc{m}^2(A,B)=N$. Note that gcd2(A,B)$gc{d}^2(A,B)$ and lcm2(A,B)$lc{m}^2(A,B)$ denote the square of gcd and the square of lcm of numbers A$A$ and B$B$ respectively.

Input Format

• The first line of input contains a single integer T$T$, denoting the number of test cases. The description of T$T$ test cases follows.

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• The only line of each test case contains an integer N$N$.

Output Format

For each test case, output in a single line, number of valid pairs (A,B)$(A,B)$.

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Constraints

• 1≤T≤105$1\le T\le {10}^5$
• 4≤N≤1010$4\le N\le {10}^{10}$