B. Sum

Codeforces

IDCF10054B

Time2000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Write a program to compute the following sum S given a positive integer n: , where is the largest integer not greater than x. The input file consists of several datasets. The first line of the input file contains the number of datasets which is a positive integer and is not greater than 30. The following lines describe the datasets. Each dataset contains a positive integer n (n ≤ 1012) written on a separate line. For each dataset, write in one line the remainder of the computed sum S divided by 106. ## Input The input file consists of several datasets. The first line of the input file contains the number of datasets which is a positive integer and is not greater than 30. The following lines describe the datasets.Each dataset contains a positive integer n (n ≤ 1012) written on a separate line. ## Output For each dataset, write in one line the remainder of the computed sum S divided by 106. [samples]

**Definitions** Let $ t \in \mathbb{Z} $ be the number of datasets. Let $ D = \{n_k \mid k \in \{1, \dots, t\}\} $ be the set of inputs, where each $ n_k \in \mathbb{Z}^+ $ and $ n_k \leq 10^{12} $. **Objective** For each $ n_k $, compute: $$ S_k = \sum_{i=1}^{n_k} \left\lfloor \frac{n_k}{i} \right\rfloor $$ Output $ S_k \bmod 10^6 $.

API Response (JSON)

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