SP34112 UDIVSUM - The Sum of Unitary Divisors

A natural number $ d $ is a unitary divisor of $ n $ if $ d $ is a divisor of $ n $ and if $ d $ and $ \frac{n}{d} $ are coprime. Let $ \sigma^{*}(n) $ be the sum of the unitary divisors of $ n $ . For example, $ \sigma^{*}(1) = 1 $ , $ \sigma^{*}(2) = 3 $ and $ \sigma^{*}(6) = 12 $ . Let $$ S(n) = \sum_{i=1}^n \sigma^{*}(i). $$ Given $ n $ , find $ S(n) \bmod 2^{64} $ .

There are multiple test cases. The first line of input contains an integer $ T $ ( $ 1 \le T \le 50000 $ ), indicating the number of test cases. For each test case: The first line contains an integer $ n $ ( $ 1 \le n \le 5 \times 10^{13} $ ).

For each test case, output a single line containing $ S(n) \bmod 2^{64} $ .