SP20174 DIVCNT3 - Counting Divisors (cube)

Let $ \sigma_0(n) $ be the number of positive divisors of $ n $ . For example, $ \sigma_0(1) = 1 $ , $ \sigma_0(2) = 2 $ and $ \sigma_0(6) = 4 $ . Let $$ S_3(n) = \sum _{i=1}^n \sigma_0(i^3). $$ Given $ N $ , find $ S_3(N) $ .

First line contains $ T $ ( $ 1 \le T \le 10000 $ ), the number of test cases. Each of the next $ T $ lines contains a single integer $ N $ . ( $ 1 \le N \le 10^{11} $ )

For each number $ N $ , output a single line containing $ S_3(N) $ .