All Tracks Problem

Buying Candies
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Very-Easy

Problem
Editorial
Analytics

A Shop sells candies in a weird way. If you buy X candies, they charge you X*num_divisors(X), where num_divisors(X) is the number of distinct divisors of X.
You need to buy candies for N kids by spending minimum money ( you should buy at least N candies ) . Print minimum money you should spend.

Input Format:-
First line will contain an integer T denoting the number of testcases.
Each test case will contain a single integer N denoting the number of kids.

Output Format:-
Output a single integer per test case in new line denoting the minimum cost.

Constraints:-
1 ≤ T ≤ 100
1 ≤ N\(10^{5}\)

SAMPLE INPUT
2
12
15
SAMPLE OUTPUT
26
34
Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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