AtCoder Beginner Contest 461
乘积为 NAI (CI翻译)
Problem Statement
题目描述
AI (CI翻译)You are given a positive integer $N$.
We call a non-empty sequence of positive integers $A$ a good sequence if it satisfies all of the following conditions:
给定一个正整数 $N$。
如果一个非空正整数序列 $A$ 满足以下所有条件，我们称它为一个好序列：AI (CI翻译)
- All elements of
$A$are distinct. - The product of all elements of
$A$equals$N$.
$A$中的所有元素互不相同。$A$中所有元素的乘积等于$N$。
The score of a sequence is defined as the sum of all elements of the sequence.
Find the sum, modulo $998244353$, of the scores of all good sequences.
一个序列的分数定义为该序列所有元素之和。
求所有好序列的分数之和，并对 $998244353$ 取模。AI (CI翻译)
Constraints
约束条件
AI (CI翻译)$1 \leq N \leq 10^{10}$- The input value is an integer.
$1 \leq N \leq 10^{10}$- 输入值为整数。
Input
输入格式
AI (CI翻译)The input is given from Standard Input in the following format:
输入从标准输入按以下格式给出：AI (CI翻译)
NNOutput
输出格式
AI (CI翻译)Output the answer on a single line.
在一行中输出答案。AI (CI翻译)
样例
Input #1
8
Output #1
80
There are $11$ good sequences: $(1,2,4),(1,4,2),(1,8),(2,1,4),(2,4),(2,4,1),(4,1,2),(4,2),(4,2,1),(8),(8,1)$.
The sum of their scores is $7+7+9+7+6+7+7+6+7+8+9=80$.
Input #2
461
Output #2
1385
Input #3
100
Output #3
1702
题目信息
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（gpt-6.1-sol），如有出入请以原文为准。