CF 1542C C. Strange Function
https://codeforces.com/problemset/problem/1542/C
题意:
定义\(f(i)\)表示最小的不能整除i的数,求\(\sum_{i=1}^nf(i)\)
若\(f(i)=x\),说明\(1|i,2|i,3|i,……(x-1)|i,x \nmid i\),即\(lcm(1,2,3,……,x-1) | i,x \nmid i\)
所以\(f(i)>=x\)的\(i\)的个数等于 \(n/lcm(1,2,3,……,x-1)\)
\(f(i)=x\)的\(i\)的个数等于 \(n/lcm(1,2,3,……,x-1)\) - \(n/lcm(1,2,3,……,x-1,x)\)
#include<bits/stdc++.h>
using namespace std;
long long getgcd(long long a,long long b)
{
return __gcd(a,b);
}
long long getlcm(long long a,long long b)
{
return a/getgcd(a,b)*b;
}
int main()
{
int T;
long long n,lcm;
const int mod=1e9+7;
int ans;
scanf("%d",&T);
while(T--)
{
scanf("%lld",&n);
ans=0;
lcm=1;
for(int i=1;;++i)
{
lcm=getlcm(i,lcm);
if(lcm>n) break;
ans+=n/lcm%mod;
ans%=mod;
}
ans=(ans+n)%mod;
printf("%d\n",ans);
}
}