Sum of NDefine 𝑓(𝑋)f(X) as the largest divisor of 𝑋X other than 𝑋X itself. For example, 𝑓(12)=6f(12)=6 and 𝑓(7)=1f(7)=1.Note that 𝑓(1)f(1) is defined to be 00.Given an integer 𝐾K, find the sum of all 𝑁N such that 𝑓(𝑁)=𝐾f(N)=K.It can be shown that the answer does not exceed 101810 18 under the given constraints.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of a single integer 𝐾K.Output FormatFor each test case, output on a new line, the sum of all 𝑁N which satisfy 𝑓(𝑁)=𝐾f(N)=K.Constraints1≤𝑇≤1041≤T≤10 4 2≤𝐾≤1062≤K≤10 6 Sample 1:InputOutput3231841536Explanation:Test Case 1 : The only number which has 𝑓(𝑁)=2f(N)=2 is 44.Test Case 2 : The only numbers which have 𝑓(𝑁)=3f(N)=3 are 66 and 99. The sum of them is 1515.

Nimisha is assigned to calculate the sum of divisors for a given positive integer. She needs a function called sumOfDivisors to calculate the sum of divisors for a given positive integer.Help her with the program.Example: If the number is 12, the sum of its divisors would be 1+2+3+4+6+12 = 28.Input format :The input consists of an integer n.Output format :The output prints the sum of all the divisors of n (inclusive).

We say that an integer 𝐷D is a divisor of another integer 𝐴A if the fraction 𝐴/𝐷A/D is also an integer. Given two positive integers 𝐴A and 𝐵B, compute the largest number which is a divisor of both 𝐴A and 𝐵B.

Number of DivisorsGiven a number, find the number of divisors of that number.Input FormatFirst line of input contains T - number of test cases. Its followed by T lines, each containing a single number N.Output FormatFor each test case, print the number of divisors of N, separated by newline.Constraints30 points1 <= T <= 1001 <= N <= 10670 points1 <= T <= 1001 <= N <= 109ExampleInput581680892397158Output416328ExplanationSelf Explanatory

You are given an integer x𝑥. Your task is to find any integer y𝑦 (1≤y<x)(1≤𝑦<𝑥) such that gcd(x,y)+ygcd(𝑥,𝑦)+𝑦 is maximum possible.Note that if there is more than one y𝑦 which satisfies the statement, you are allowed to find any.gcd(a,b)gcd(𝑎,𝑏) is the Greatest Common Divisor of a𝑎 and b𝑏. For example, gcd(6,4)=2gcd(6,4)=2.InputThe first line contains a single integer t𝑡 (1≤t≤10001≤𝑡≤1000) — the number of test cases.Each of the following t𝑡 lines contains a single integer x𝑥 (2≤x≤10002≤𝑥≤1000).OutputFor each test case, output any y𝑦 (1≤y<x1≤𝑦<𝑥), which satisfies the statement.ExampleinputCopy710721100210006outputCopy56189817503

Given an integer N, find the maximum sum that you can get from the following series: 1*2 - 2*3 + 3*4 - 4*5 .... K*(K+1), where K<=N.Input FormatThe first line of input contains T - the number of test cases. It is followed by T lines, each contains a single integer N.Output FormatFor each test case, print the result, separated by a newline.Constraints30 points1 <= T <= 1001 <= N <= 10070 points1 <= T <= 1051 <= N <= 109ExampleInput235Output818