Online JudgeProblem SetAuthorsOnline ContestsUser
Web Board
Home Page
F.A.Qs
Statistical Charts
Problems
Submit Problem
Online Status
Prob.ID:
Register
Update your info
Authors ranklist
Current Contest
Past Contests
Scheduled Contests
Award Contest
User ID:
Password:
  Register

母函数方法求出的,求论证。。。

Posted by slp at 2010-08-01 14:46:13 on Problem 3604
http://hi.baidu.com/sulipol/blog/item/0ace8af56765aad4f3d385ee.html
定义函数h(x)=g(pi^x)=(x+1)^3
为了简化函数,定义函数h(x)=g(pi^x)=(x+1)^3

求一个数n的每个因子的.因子个数的三次方的和的母函数如下:


(h(0)*p1^0 + h(1)*p1^1 + ... + h(k1)*p1^k1)*...*( h(0)pi^0 + h(1)pi^1 + ... + h(i)pi^ki


这时总的方案数ss=(h(0)+h(1)+...+h(k1))*...*(h(1)+h(2)+...+h(ki))


再利用求和公式1^3 + 2^3 + …… n^3 = [n (n+1) / 2]^2

可得ss=PI[(ki+1)(ki+2)/2]^2 ,(PI代表连乘符号)

MORE:http://hi.baidu.com/sulipol/blog/item/0ace8af56765aad4f3d385ee.html

Followed by:

Post your reply here:
User ID:
Password:
Title:

Content:

Home Page   Go Back  To top


All Rights Reserved 2003-2013 Ying Fuchen,Xu Pengcheng,Xie Di
Any problem, Please Contact Administrator