The mathematical problem of "Euler function" Bzoj2190-[sdoi2012]longge

"The main topic"

Find out ∑GCD (i, N) (1<=i <=n).

Ideas

For X=AK,Y=BK, gcd (A, B) =1 must have gcd (x, y) = 1. All factors of the enumeration N, ∑GCD (i, N) =∑ (φ (n/k) *k) (k| N).

*n factor and must be in the n^ (1/2) time to find out, otherwise it will tle.

Code

1#include <iostream>2#include <cstdio>3#include <cstring>4#include <algorithm>5 using namespacestd;6typedefLong Longll;7 /*Note Data range*/8 Const intmaxn=10010;9 ll N;Ten ll FACTOR[MAXN]; One   A voidGet_factor () - /*all quality factors must be calculated within n^ (1/2) time, otherwise te*/ - { theMemset (Factor,0,sizeof(factor)); - ll I; -      for(i=1; i*i<n;i++) -     { +         if(n%i==0) -         { +factor[++factor[0]]=i; Afactor[++factor[0]]=n/i; at         } -     } -     if(i*i==n) factor[++factor[0]]=i; - } -   - ll Eular (ll K) in { -ll res=K; to      for(LL p=2;p *p<=k;p++) +     { -         if(k%p==0) the         { *res=res-res/p; $              while(k%p==0) k/=p;Panax Notoginseng         } -     } the     if(k>1) res=res-res/K; +     /*idea K may be greater than 0 and must be subtracted*/ A     returnRes; the } +   - voidInit () $ { $scanf"%d",&n); - } -   the ll Get_ans () - {Wuyill result=0; the      for(LL i=1; i<=factor[0];i++) -Result+=eular (N/factor[i]) *Factor[i]; Wu     returnresult; - } About   $ intMain () - { - init (); - get_factor (); ACout<<get_ans () <<Endl; +     return 0; the}

The mathematical problem of "Euler function" Bzoj2190-[sdoi2012]longge