No.3505 Sum of Prod of Root
Solalyth
Naru820
Nzt3
問題文最終更新日: 2026-04-17 21:03:55
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CPCTF 2026: PPC
(順位表)
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Problem Statement
You are given a positive integer $N$. Output the remainder when the integer $\displaystyle \sum_{i=1}^N \prod_{k=1}^{\infty} \lfloor \sqrt[k]{i} \rfloor$ is divided by $998244353$.
Constraints
- $1 \leq N \leq 10^{18}$
- All inputs are integers.
Input
The input is given from standard input in the following format.
$N$
Output
Output on a single line the remainder when the desired integer is divided by $998244353$.
Sample
Sample 1
Input
6
Output
36
We have $\displaystyle \sum_{i=1}^6 \prod_{k=1}^{\infty} \lfloor \sqrt[k]{i} \rfloor = 1 + 2 + 3 + 8 + 10 + 12 = 36$.
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