题目大意 \(t\)组询问, 每组询问给定\(n\),求\(\sum_{k=1}^n[n,k]\),其中\([a,b]\)表示\(a\)和\(b\)的最小公倍数 . \(t\leq 300000,n\leq 1000000\) 题解 \[ \begin{align} \sum_{k=1}^n[k,n]&=n\sum_{k=1}^n\frac{k}{(k,n)}\\ &=n\sum_{p|n}\frac{1}{p}\sum_{k=1}^nk[(k,n)=p]\\ &=n\sum_{p…

GCD and LCM Time Limit: 20 Sec Memory Limit: 256 MB 题目连接 http://acm.hdu.edu.cn/showproblem.php?pid=4497 Description Given two positive integers G and L, could you tell me how many solutions of (x, y, z) there are, satisfying that gcd(x, y, z) = G and…

题意:给你一个正整数\(x\),找两个正整数\(a\),\(b\),使得\(lcm(a,b)=x\),并且\(max(a,b)\)最小. 题解:我们知道,\(lcm(a,b)=a*b/gcd(a,b)\),所以如果\(a\)和\(b\)不互质,那么\(a*b\)必然可以约去一个\(gcd(a,b)\),也就表示\(max(a,b)\)的值可以变得更小,所以我们要找的\(a\)和\(b\)必然要互质,即得到\(gcd(a,b)=1\),从而推出\(a*b=x\),所以我们可以直接枚举到\(\sqr…

题意:给你一个数列,求所有子序列对的\(lcm\),然后求这些所有\(lcm\)的\(gcd\). 题解:我们对所有数分解质因数,这里我们首先要知道一个定理: ​ 对于\(n\)个数,假如某个质数\(p\),这\(n\)个数中有\(\le n-1\)个数的质因数包含\(p\),那么他们的\(lcm\)中一定不含\(p\)这个因数,随意我们先预处理出每个数的质因子,选择个数\(\ge n-1\)的质因子. ​ 然后,在这些质因子中,我们要求每两两之间的\(lcm\),然后再求他们的\(gcd\),…

发信人: fennec (fennec), 信区: Algorithm 标 题: acm 总结 by fennec 发信站: 吉林大学牡丹园站 (Wed Dec 8 16:27:55 2004) ACM总结(fennec) 其实在北京比赛完的时候,我就想写了,不过还是早了点,直到上海比赛结束,大家的心中都不是太好受.郭老师有句话:你们这样做也是对的,不成功就成仁.让我的心也能安慰了不少. 我是从大一下学期开始接触ACM的,那时候我们学校才刚刚起步,siyee,wjiang师兄可以说是我的领路人了…

 LCM Challenge Time Limit:1000MS     Memory Limit:64000KB     64bit IO Format:%lld & %llu Submit Status Practice ACdream 1077 Description Some days ago, I learned the concept of LCM (least common multiple). I've played with it for several times and I…

A pair of numbers has a unique LCM but a single number can be the LCM of more than one possiblepairs. For example 12 is the LCM of (1, 12), (2, 12), (3,4) etc. For a given positive integer N, thenumber of different integer pairs with LCM is equal to N…

LCM Walk Time Limit: 20 Sec Memory Limit: 256 MB 题目连接 http://acm.hdu.edu.cn/showproblem.php?pid=5584 Description A frog has just learned some number theory, and can't wait to show his ability to his girlfriend. Now the frog is sitting on a grid map o…

C. The Big Race Time Limit: 20 Sec Memory Limit: 256 MB 题目连接 http://codeforces.com/contest/592/problem/C Description Vector Willman and Array Bolt are the two most famous athletes of Byteforces. They are going to compete in a race with a distance of…

Problem Description A frog has just learned some number theory, and can't wait to show his ability to his girlfriend. Now the frog ,,⋯ from the bottom, so are the columns. At first the frog is sitting at grid (sx,sy), and begins his journey. To show…