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Time Limit: 2 s Memory Limit: 256 MB Total points: 100

#22586. 睡前阅读 II

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复原题面:未能找回原始英文题目页面。本版本根据官方分析和存档输入输出数据重建。

Farmer John 继续为 Bessie 做数论睡前阅读。对正整数 $n$,令 $s(n)$ 为其真因数之和,即所有小于 $n$ 的正因数之和。反复应用 $s$ 得到约数和序列。例如从 $12$ 开始得到 $12, 16, 15, 9, 4, 3, 1$。

从 $n$ 开始的循环是最终返回 $n$ 的序列。对给定闭区间内每个起始整数,如果序列在先遇到更小整数之前返回它,就找出并输出循环。每个循环只输出一次,以其起始整数开始。循环中可以有大于输入区间上界的数。

输入格式

  • 第 $1$ 行:两个整数 $A$、$B$ $(1 \le A \le B \le 2,000,000)$。

输出格式

对输入区间内每个约数和序列在遇到更小值之前返回自身的起始整数,输出一行序列,整数间用空格分隔。

样例

输入格式 1

200 1200

输出格式 1

220 284
496
1184 1210

题目来源:传统题;年份:2006。

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