hdu 4228 反素数

反素数

Defination:

反素数
对于任何正整数x,起约数的个数记做g(x).例如g(1)=1,g(6)=4.
如果某个正整数x满足:对于任意i(0<i<x),都有g(i)<g(x),则称x为反素数.

Property:

1. 一个反素数的所有质因子必然是从2开始的连续若干个质数，因为反素数是保证约数个数为的这个数尽量小
2. 同样的道理，如果n=2t1×3t2×5t3×⋯ptkk，那么必有t1≥t2≥t3≥⋯≥tk

据说。。。
在ACM竞赛中，最常见的问题如下：
（1）给定一个数，求一个最小的正整数，使得的约数个数为
（2）求出中约数个数最多的这个数

Problem

You want to decorate your floor with square tiles. You like rectangles. With six square flooring tiles, you can form exactly two unique rectangles that use all of the tiles: 1x6, and 2x3 (6x1 is considered the same as 1x6. Likewise, 3x2 is the same as 2x3). You can also form exactly two unique rectangles with four square tiles, using all of the tiles: 1x4, and 2x2.
Given an integer N, what is the smallest number of square tiles needed to be able to make exactly N unique rectangles, and no more, using all of the tiles? If N=2, the answer is 4.

Input
There will be several test cases in the input. Each test case will consist of a single line containing a single integer N (1 ≤ N ≤ 75), which represents the number of desired rectangles. The input will end with a line with a single 0.

Output
For each test case, output a single integer on its own line, representing the smallest number of square flooring tiles needed to be able to form exactly N rectangles, and no more, using all of the tiles. The answer is guaranteed to be at most 10^18. Output no extra spaces, and do not separate answers with blank lines.

Solution